Algebra inequality

Question

provide 2 different solution methods

Chocolate Bliss sells their box of chocolate candy for $2.00 per candy plus a $12 packaging fee. Expressions in Sweets sell their box of chocolate candy for $3.00 per candy plus a $10 packaging fee. If five boxes of Chocolate Bliss chocolate candy cost the same as four boxes of Expressions in Sweets chocolate candy, how many candies are in each box?

Answer 1

Prices per box:

Chocolate Bliss:

y_cb = 2x+12

Expression in sweets:

y_es = 3x+10

Where x is the number of candies

They are wanting the the number of candies in a box when the price of 5 boxes of CB costs the same as 4 boxes of ES.

5y_cb=4y_es

5(2x+12)=4(3x+10)

10x+60 = 12x+40

2x=20

x = 10 pieces of candy per box

The total price from either candy store = 5(20+12) = 100+60 = $160.

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Another method

5(2x+12)=10x+60=P, P = price

4(3x+10)=12x+40=P

Subtract the 2 equations

-2x+20=0

-2x=-20

x=10

P = 12(10)+40 = 120+40 = $160

Answer 2

Assuming the same number of each candy is in each box:

c represents the number of candies in each box

For bliss the cost is (5)(2c) + 12

For sweets the cost is (4)(3c) + 10

(5)(2c) + 12 = (4)(3c) + 10

10c + 12 = 12c + 10

2 = 2c

1 = c

Sounds silly that each box contains only one candy. Please review the post for accuracy.