Answer:
The cost of a can of popcorn is $10.
The cost of a box of cookies is $5.
The cost of a can of popcorn is $20
Step-by-step explanation:
First you must propose a system of equations, a set of two or more equations with several unknowns in which you want to find the value of each unknown so that all the equations of the system are fulfilled.
Defining the variables:
x: cost of one pound of candyy: cost of a box of cookiesz: cost of a can of popcornAmy sold 2 pounds of candy, 3 boxes of cookies and 1 can of popcorn for a total sale of $65. Then:
2*x + 3*y + 1*z=65 Equation 1
Brian sold 4 pounds of candy, 6 boxes of cookies and 3 cans of popcorn for a total sale of $140. So:
4*x + 6*y + 3*z=140 Equation 2
Paulina sold 8 pounds of candy, 8 boxes of cookies and 5 cans of popcorn for a total sales of $250. Then:
8*x + 8*y + 5*z=250 Equation 3
Then the system of equations is formed by these three equations.
A method to solve a system of equations is by means of the substitution method, which consists of isolating one of the two unknowns in an equation to substitute it in the other equation.
Isolating z from Equation 1:
[tex]z=65-2*x-3*y[/tex] Equation 4
Replacing in Equation 2:
4*x + 6*y + 3*(65 -2*x-3*y)=140
4*x + 6*y + 195 - 6*x - 9*y= 140
-2*x - 3*y=140-195
-2*x - 3*y=-55
2*x + 3*y= 55
and isolating x:
[tex]x=\frac{55-3*y}{2}[/tex] Equation 5
Replacing in Equation 4:
[tex]z=65-2*\frac{55-3*y}{2} -3*y[/tex]
z=65 - (55-3*y) - 3*y
z= 65 -55 + 3*y - 3*y
z= 10
So the cost of a can of popcorn is $10.
Replacing equation 5 and the value of z in equation 3:
8*[tex]\frac{55-3*y}{2}[/tex] + 8*y + 5*10=250
[tex]\frac{8}{2}[/tex]*(55 -3*y)+ 8*y + 5*10=250
4*(55 -3*y)+ 8*y + 5*10=250
4*55 - 4*3*y + 8*y + 50=250
220 - 12*y + 8*y + 50=250
-12*y + 8*y= 250 -220 - 50
-4*y= -20
[tex]y=\frac{-20}{-4}[/tex]
y= 5
So the cost of a box of cookies is $5.
Finally replacing the value of y in Equation 5 you get the value of x:
[tex]x=\frac{55-3*5}{2}[/tex]
[tex]x=\frac{55-15}{2}[/tex]
[tex]x=\frac{40}{2}[/tex]
x=20
Finally, the cost of a can of popcorn is $20
Simplify the following - (32)²
Answer:
=-1024
Step-by-step explanation:
Hope this helps (:
What is the most important variable in the problem?
An auto shop has 98 cans of oil at the beginning of the day. 12 hours later, there are 10 cans remaining. How many were sold?
Answer:
Step-by-step explanation:
There are two if you want to answer the question. You have to know the starting value, and you have to know the ending value.
The question asks how many cans were sold. You can't answer that without knowing what you started with and what you ended with.
98 - 10 = 88
Sarah and her children went into a movie theater where they sell bags of popcorn for $7.50 each and drinks for $4.50 each. Sarah has $90 to spend and must buy a minimum of 16 bags of popcorn and drinks altogether. If xx represents the number of bags of popcorn purchased and yy represents the number of drinks purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
A possible solution is she should by 6 bags of popcorn and 10 drinks
Step-by-step explanation:
The price of each bag of popcorn = $7.50
The price of each drink = $4.50
The amount Sarah has to spend = $90
The number of bags of popcorn and drinks Sarah must buy = 16 bags of popcorn and drinks
Let the number of bags of popcorn purchased be represented by x and the number of drinks purchased be represented by y
Therefore, we have;
x + y ≥ 16.....(1)
x × 7.5 + y × 4.5 ≤ 90
Which gives;
7.5·x + 4.5·y ≤ 90....(2)
Rewriting the inequalities as a function of y, gives;
From inequality (1), x + y ≥ 16, we have;
y = ≥ 16 - x
From inequality (2), 7.5·x + 4.5·y ≤ 90, we have;
7.5·x + 4.5·y ≤ 90
4.5·y ≤ 90 - 7.5·x
y ≤ 90/4.5 - 7.5/4.5·x
y ≤ 20 - 5/3·x
Please find attached, the plot of the inequalities
A possible solution is given as the value of x = 6, where y = 10
Therefore, she should by 6 bags of popcorn and 10 drinks.
During the bake sale, Paayal and Parvathy sold 200 cookies. Paayal sold her cookies for 5 cents each, while Parvathy sold her cookies for 10 cents each. The total amount of money customers paid for cookies was $11.00. How many cookies did Paayal sell? How many cookies did Parvathy sell?
Answer:
Paayal sold 180 cookies and Parvathy sold 20 cookies.
Step-by-step explanation:
From the information given, you can write the following equations:
x+y=200 (1)
0.05x+0.10y=11 (2), where:
x is the amount of cookies that Paayal sold and y is the amount of cookies that Parvathy sold.
First, you can solve for x in (1):
x=200-y (3)
Now, you can replace (3) in (2):
0.05(200-y)+0.10y=11
10-0.05y+0.10y=11
0.05y=1
y=1/0.05
y=20
Finally, you can replace the value of y in (3) to find x:
x=200-y
x=200-20
x=180
According to this, the answer is that Paayal sold 180 cookies and Parvathy sold 20 cookies.
Please help me this question is hard
Answer:
I cant see
Step-by-step explanation:
Answer:
dont have an answer yet...question too small to see...
Step-by-step explanation:
30 POINTS! HELP ME PLZZ I NEED HELP WITH THIS!!!
Answer:3/12 is greater
Step-by-step explanation:
Since 3/12 and 2/9 have different denominators, you need to find the Least Common Multiple (LCM) of the denominators and then multiply the top and bottom of each fraction by the number of times the denominator goes into the LCM.
According to my calculations, the LCM of the two denominators is 36. Therefore, since 12 goes into 36 a total of 3 times, you would multiply the top and bottom of the first fraction by 3. And since 9 goes into 36 a total of 4 times, you would multiply the top and bottom of the second fraction by 4.
Step #2: Now that the denominators are the same, you can simply compare the numerators to determine which fraction is greater. Since 9 is greater than 8, 9/36 is greater than 8/36. Therefore the 1st entry (3/12) is greater than the 2nd entry (2/9).
i need help with fractions :(
Answer:
x = 0, Need the steps?
STEPS:
9x - 7 = -7 (Original Problem)
9x = 0 (Add 7 to both sides)
x = 0 (Divide both sides by 9)
Answer:
Step-by-step explanation:
(3) 9x-7=7
First multiply 3 by 9x to get 27x
27x-7=7
Then add 7 to both sides
27x-7+7=7+7
27x=14
27x/27=14/27
x=14/27
A can run 3 miles in 30 minutes. How long will it take
the runner to run 2.5 miles? Use the diagram to explain.
Answer:
It will take her about 25 minutes.
Step-by-step explanation:
30 divided by 3 is ten.
It takes ten minutes to run each miles.
I don't have a diagram, but try drawing a graph with the information.
7+ (-5)+(-2)=0
7+ (5)+(2)=0
7+(-4)+(-3)=0
7+(-6)+(-1)=0
Answer:
1. true
2. false
3. true
4. true
What is the difference between slope and average rate of change ?
Find the volume of this object. Use 3 for pi. (CAN ANYONE HeLP:))
Step-by-step explanation:
sorry for the rough handwriting but that's that
17z = 16z − 15 whats z ?
Answer:
z = -15
Step-by-step explanation:
17z = 16z − 15
Subtract 16z from each side
17z-16z = 16z-16z − 15
z = -15
what is the slope of a line perpendicular to the line whose equation is 9x+3y=-27
Answer:
y = (1/3)x - 27 <-- perpendicular line
Step-by-step explanation:
9x + 3y = (-27)
3x + y = (-27)
y = (-3x) - 27 <-- original line
y = (-3x) - 27 <-- original line
slope = (-3)
slope = (-3/1)
inverse = (1/-3)
negative inverse = (1/3)
y = (1/3)x - 27 <-- perpendicular line
Which description matches DIAGRAM A?
A An increase by 2/3
B An increase by 5/6
C A decrease by 2/5
D A decrease by 5/11
the answer is d a decrease by 5/11
plz help asap nowwww
Answer:
10 to the power of 5 is 50 so do 50 times 3.8 and 10 to the power of 4 is 40 so do 40 times 5.9
for a giveaway, a local radio station is putting together goodie bags. The bags will include tickets and posters. Each goodie bag will receive an equal share of 54 tickets and 36 posters.
(A) what is the greatest number of goodie bags that can be created? explain your reasoning.
(B) How many of each type of giveaway will be in each bag? Explain your reasoning.
You are making some chili and need some onions and peppers. One pound of onions costs $0.97 and one pound of peppers cost $1.30. What is the total cost of 0.76 pounds of onions and 1.5 pounds of peppers? The total cost of 0.76 pounds of onions and 1.5 pounds of peppers is $
Answer:
The cost of 0.76 pounds of onion is [tex]x = \$ 0.988 [/tex]
The cost of 1.5 pounds of peppers is [tex] y = \$ 1.455[/tex]
The total cost is [tex]z = \$ 2.443 [/tex]
Step-by-step explanation:
From the question we are told that
The cost of one pound of pepper is C = $0.97
The cost of one pound of onion is [tex]C_o = \$ 1.30[/tex]
Generally the cost of 0.76 pound of onion is mathematically represented as
[tex]x = \frac{0.76 * 1.30}{1}[/tex]
=> [tex]x = \$ 0.988 [/tex]
Generally the cost of 1.5pound of peppers is mathematically represented as
[tex] y = \frac{1.5 * 0.97}{1}[/tex]
=> [tex] y = \$ 1.455[/tex]
The total cost of 0.76 pounds of onions and 1.5 pounds of peppers is
[tex]z = x+ y[/tex]
=> [tex]z = 0.988 + 1.455 [/tex]
=> [tex]z = \$ 2.443 [/tex]
(1,6) (3,4) what’s the slope?
Answer: m = -1
The slope is -1
Plz mark brainliest:)
2. Determine the amount of interest owed after 2 years on a $850 loan at 12.25% if no payments
are made. LTD
Enter your answer
The amount of interest is 208.74$
Here we have given
Amount (P)=850$
Interest (r)=12.25%
Time (t)=2 years
we have to calculate the simple interest
What is the formula for simple interest?
[tex]I=\frac{PRT}{100}[/tex]
Plug the given value in above formula
[tex]I=\frac{850*12.25*2}{100}[/tex]
Simplify above equation we get
[tex]I=\frac{850*12.25*2}{100}\\\\I=\frac{20874}{100}\\\\I=208.74[/tex]
Therefore the amount of interest is 208.74$
To learn more about the interest visit:
https://brainly.com/question/25793394
Please help please help
What is the slope of the line that passes through the points (-5,7) and (10, 1)?
А
m = 5/2
B
m = -5/2
С
m = -2/5
D
m = 2/5
The points are (-5,7) and (10,1). The slope of the points is -2/5.
How to calculate a slope ?Any two different points on a line can be used to calculate the slope of any line. The slope of a line formula is used to determine the ratio of "vertical change" to "horizontal change" between two different points on a line.
Given that,
The points are (-5,7) and (10,1).
We have to find the slope of the points.
The relationship between how a line's y coordinate changes and how its x coordinate changes determines a line's slope. y and x are the net changes in the y and x coordinates, respectively. As a result, the change in y coordinate with regard to the change in x coordinate can be written as,
Slope of the points=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Here,
x₁=-5,
y₁=7
x₂=10
y₂=1
Slope of the points [tex]= \frac{1 - 7}{10 + 5}[/tex]
Slope of the points =(-6)/(15)
Slope of the points = -2/5
Therefore, the slope of the points is -2/5.
To learn more about slope visit: https://brainly.com/question/3605446
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Help asap!!
Jenny predicted that she would sell 12 bracelets, but she actually sold 16 bracelets. Which expression would find the percent error? Use the table below to help answer the question.
Percent Error
Item
Approximate value
Exact value
Error
Absolute error
Ratio
Percent error
Bracelets
12
16
–4
4
-4/12(100)
-4/12
4/16
4/16(100)
4/16(100)
Step-by-step explanation:
Answer:
4/16(100)
Step-by-step explanation:
Lucia wishes to advertise her business, so she gives packs of 6 red flyers to each restaurant owner and sets of 4 blue flyers to each clothing store owner. At the end of the day, Lucia realizes that she gave out the same number of red and blue flyers. What is the minimum number of flyers of each color? Flyers
Answer:
12
Step-by-step explanation:
No. of red flyers = 6
No. of blue flyers = 4
We need to find the minimum number of flyers of each color if she gave out the same number of red and blue flyers. For this we must find the LCM of 6 and 4.
Prime factorization of 6 = 2×3
Prime factorization of 4 = 2×2
Lowest common multiple of 6 and 4 = 12
Hence, there are 12 minimum number of flyers of each color
If a population roughly doubles in the course of 22 years, its growth rate would be close to
C) 2.0
A) 1.5
D) 3.2
B) 1.2
Answer:
hmm you need help
Step-by-step explanation:
2-83. Build, simplify, and solve each equation. Record your work. Drag the tiles below into the equation mat.
a. -x+ 2 = 4
Answer:
you need to add 2 to the x and convert it to negative X=-2
Step-by-step explanation:
Doug's Pizza Shop sells pizza for $12plus $3per topping "t". Jake'sPizza Shop sells pizza for $17plus $2per topping "t". Write an equation that willtell you how many toppings need to be on a pizza from each pizza place to make their pizza the same price.
Answer:
5 toppings
Step-by-step explanation:
Given that :
Doug's pizza:
Sales price of pizza :$12 plus
Topping (t) = $3 per topping
Jake's pizza:
Sales price of pizza :$17 plus
Topping (t) = $2 per topping
To make their pizza the same price, how many topping needs to be on a pizza of each
12 + 3t = 17 + 2t
3t - 2t = 17 - 12
t = 5
5 toppings each
Please help! I will give brainliest!
15 points!!!
Answer:
1887
Step-by-step explanation:
[tex]\textrm{substitute }x=-5\textrm{ into the equation:}\\2(-5)^{4}-5(-5)^{3}+(-5)^{2}+3(-5)+2\\=2(625)-5(-125)+25-15+2\\=1887[/tex]
michael jordan only has 1.8 pieces of greatest of all time
and lebron james has 8.48 pieces of greatest of all time
answer 8.48 x 1.8 when you get the answer add it woth 8.48 and 1.8
will give brainliest
Answer:
25.544
Step-by-step explanation:
Which of the following is equal to 4 1/2 ÷ 2 2/3 ??? I need help answering this question.
Answer:
27/16 the same as 1 11/16
Step-by-step explanation:
First, make it an improper fraction:
9/2 ÷ 8/3
now flip the second number and multiply across:
9/2 × 3/8 = 27/16
After completing the fraction division 5 divided by five-thirds, Miko used the multiplication shown to check her work. 3 times five-thirds = StartFraction 3 Over 1 EndFraction times five-thirds = StartFraction 15 Over 3 EndFraction or 5 Which is the most accurate description of Miko's work?
Step-by-step explanation:
5 divided by five-thirds can be written in the fractional form is as follows :
[tex]\dfrac{5}{\dfrac{5}{3}}[/tex]
It can be also written as :
[tex]\dfrac{5}{\dfrac{5}{3}}=5\times \dfrac{3}{5}\\\\=3[/tex]
He has done calculations as follows :
3 x 5/3=3/1 x 5/3 = 15/3 or 5
Miko was wrong in the first step where he multiplied 3 by (5/3). It should be 5 multiplied by (3/5). He has done multiplication incorrectly.
Answer: A
Step-by-step explanation: i took the test