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A school is having a valentine's day sale. The first day,they sold 20 roses and 15 boxes of chocolate for $80. The second day they sold 40 roses and 20 boxes of chocolate for $120. How much were the roses and how much were the boxes of chocolate?

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Answer:

roses were $1 each and chocolates were $4 per box

Step-by-step explanation:

let Cost of 1 rose = "R" and Cost of 1 box of chocolate = "C"

First day: cost of 20 roses + cost of 15 chocolate = $80,

or...

20R + 15C = 80  (divide both sides by 5)

4R + 3C = 16 ------------(eq 1)

Second day: cost of 40 roses + cost of 20 chocolate = $120,

or...

40R + 20C = 120  (divide both sides by 10)

4R + 2C = 12 ------------(eq 2)

by elimination, (eq 1) - (eq 2)

(4R + 3C) - (4R + 2C) = 16 - 12

4R + 3C - 4R - 2C = 4

C = 4  (substitute this back into eq 1)

4R + 3(4) = 16

4R + 12 = 16

4R = 16 - 12

4R = 4

R = 1

Hence roses were $1 each and chocolates were $4 per box

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