Question

At a store, 3 pieces of cake and 4 pieces of bread together

cost $18.60. The total cost of 2 pieces of cake and 2 glasses of
juice is $12.34. If one piece of cake costs 2 times as much as
one piece of bread, what is the total cost of 5 pieces of cake
and 4 glasses of juice? Include two decimal places in your
answer. For example if the answer is $12 enter it as $12.00.

Answer 1

9514 1404 393

Answer:

$28.40

Explanation:

Using the given information, we can write three equations relating the three item prices. Let c, b, and j represent the cost of 1 item each of cake, bread, and juice.

3c +4b = 18.60

2c +2j = 12.34

c = 2b

Multiplying the third equation by 2 gives an expression for 4b that we can substitute into the first equation.

2c = 4b

3c +2c = 18.60

c = 18.60/5 = 3.72

Doubling the second equation almost gives us the purchase we want.

2(2c +2j) = 2(12.34)

4c +4j = 24.68

Adding one more cake to this give the desired purchase:

(4c +4j) +c = 24.68 +3.72

5c +4j = 28.40

The total cost of 5 pieces of cake and 4 glasses of juice is $28.40.