Tara's website, verdantveggies.com, specializes in the sale of rare or unusual vegetable seeds. Tara sells packets of sweet-pepper seeds for $2.85 each and packets of hot-pepper seeds for $4.29 each. She also offers a 16-packet mixed-pepper assortment combining packets of both types of seeds at $3.30 per packet. How many packets of each type of seed are in the assortment?​

Answer:

Let's define the variables:

S = # of sweet pepper seeds in the mix pack.

H = # of hot pepper seeds in the mix pack.

Let's suppose that $3.30 is the mean price of the seeds in the mix pack.

Then we have two equations:

S + H = 16.

(S*$2.85 + H*$4.29)/16 = $3.30

Now let's solve this system.

The first step is isolating one variable in one of the equations, i will isolate S in the first equation.

S = 16 - H.

Now we can replace this in the second equation, and solve it for H.

( (16 - H)*$2.85 + H*$4.29)/16 = $3.30

( (16 - H)*$2.85 + H*$4.29) = $3.30*16 = $52.80

$45.60 + H*$1.44 = $52.80

H*$1.44 = $52.80 - $45.60 = $7.20

H = $7.20/$1.44 = 5

Then in the mix pack there are 5 hot-pepper seeds.

And the other 11 must be sweet-pepper seeds

Algebraic equations are equations that contain unknown variables.

The number of packets of sweet-pepper seeds is 11 and the number of packets of hot-pepper seeds is 5.

Let's represent:is

The number of packets of sweet-pepper seeds = s

The number of packets of hot-pepper seeds = h

Based on this question, our system of equations are:

$2.85 x s + $4.29 x h = $3.30(16)

2.85s + 4.29h = 52.8...........Equation 1

s + h = 16...........Equation 2

s = 16 - h

We substitute 16 - h for s in Equation 1

2.85(16 - h) + 4.29h = 52.8

45.6 -2.85h + 4.29h = 52.8

Subtract 45.6 from both sides

45.6 - 45.6 -2.85h + 4.29h = 52.8 - 45.6

1.44h = 7.2

h = 5

There are 5 hot-pepper seeds in the assortment.

Solving for the number of sweet-pepper seeds.

s = 16 - h

s = 16 - 5

s = 11

There are 11 sweet-pepper seeds in the assortment.

Therefore, the number of packets of sweet-pepper seeds is 11 and the number of packets of hot-pepper seeds is 5.

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