SOLUTION: matt and ming are selling fruit for a school fundraiser. customers can buy small boxes of oranges and large boxes of oranges. matt sold 3 small boxes and 14 large boxes of oranges

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Question 271268: matt and ming are selling fruit for a school fundraiser. customers can buy small boxes of oranges and large boxes of oranges. matt sold 3 small boxes and 14 large boxes of oranges for a total of $203. ming sold 11 small boxes and 11 large boxes of oranges for a total of $220. find the cost of each one small box and one large box of oranges.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = cost of one small box
Let b = cost of one large box
given:
(1) 3a+%2B+14b+=+203
(2) 11a+%2B+11b+=+220
Multiply both sides of (2) by 3%2F11
(1) 3a+%2B+14b+=+203
(2) %283%2F11%29%2A11a+%2B+%283%2F11%29%2A11b+=+%283%2F11%29%2A220
And subtract (2 ) from (1)
(1) 3a+%2B+14b+=+203
(2) -3a+-+3b+=+-60
11b+=+143
b+=+13
and, since
3a+%2B+14b+=+203
3a+%2B+14%2A13+=+203
3a+%2B+182+=+203
3a+=+21
a+=+7
The cost of 1 small box is $7
The cost of 1 large box is $13
check:
(2) 11a+%2B+11b+=+220
a+%2B+b+=+20
13+%2B+7+=+20
20+=+20
OK