SOLUTION: Tom and Jerry are selling fruit for a charity fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Tom sold 3 small boxes of oranges and 14 large boxes
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Question 1168273: Tom and Jerry are selling fruit for a charity fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Tom sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Jerry sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges. Found 2 solutions by josgarithmetic, greenestamps:Answer by josgarithmetic(39617) (Show Source):
This is a good problem for demonstrating that the formal algebraic solution follows exactly the same path as an informal solution using logical reasoning and simple arithmetic.
(1) Given:
3 small and 14 large sell for $203
11 small and 11 large sell for $220
Algebraically:
(2) Logical reasoning: if 11 of each cost $220, then 1 of each costs $220/11 = $20.
Algebraically:
(3) Logical reasoning: if 1 of each costs $20, then 3 of each cost $60.
Algebraically:
(4) Logical reasoning: If the numbers of small boxes are the same, then the difference in cost is because of the difference in the numbers of large boxes. The difference in cost is $143; that is because of the 11 additional large boxes.
Algebraically (subtracting one equation from the other):
(5) Logical reasoning: If 11 large boxes cost $143, then each large box costs $143/11 = $13.
Algebraically:
(6) Logical reasoning: 1 of each costs $20; and the large box costs $13; so the small box costs $20-13 = 7.
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