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Question 1184380: Jane paid $112 for 2 identical cups and 3 identical bowls. Each cup cost 1/2 as much as each bowl. Find the cost of each bowl.
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
Informally, using logical reasoning and common sense....
Since the cost of each cup is half the cost of each bowl, the cost of 2 cups is the same as the cost of 1 bowl. So buying 2 cups and 3 bowls costs the same as buying 1+3=4 bowls.
Since she paid $112, the cost of each bowl was $112/4 = $28.
ANSWER: $28 for each bowl
With formal algebra....
b = # of bowls
c = # of cups
3b+2c=112 [1] the cost of 3 bowls and 2 cups was $112
c=(1/2)b [2] each cup costs half as much as each bowl
Substitute [2] into [1]:
3b+2((1/2)b) = 112
3b+b = 112
4b = 112
b = 112/4 = 28
As you see, the formal algebraic solution follows exactly the same path as the informal one.
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