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 of oranges and 14 large box

Question 831258: 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 of oranges and 14 large boxes of oranges for a total of $203. Ming 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 Elomeht, jgr45:
Answer by Elomeht(22) (Show Source): You can put this solution on YOUR website!
1. 3x + 14y = 203
2. 11x + 11y = 220
3. Divide the last equation above by 11: x + y = 20
4. This is the same as saying x = 20 - y
5. Now, substitute for x in the first equation: 3(20 - y) + 14y = 203
6. The above equation simplifies to 60 - 3y + 14y = 203
7. Now express the equation in terms of y: 11y = 143
8. From the last equation, y = 13
9. Since x + y = 20, x = 7
10. Check: (3 times 7) + (14 times 13) = 21 + 182 = 203;
(11 times 7) + (11 times 13) = 77 + 143 = 220
Answer by jgr45(31) (Show Source): You can put this solution on YOUR website!
What you need to do here is somehow isolate one of the variables.
3x + 14y = 203
11x + 11y = 220
What I would do here is first of all divide the bottom equation by 11:
x + y = 20
Now get one variable by itself. Either one works; I'll choose y.
y = 20 - x
Now substitute 20-x for y in either equation. I'll pick the first one.
3x + 14(20-x) = 203
3x + 280 - 14x = 203
280 - 11x = 203
280 = 203 + 11x
77 = 11x
x = 7
Which means y = 20-7 or 13.
So your prices are $7 for the small boxes and $13 for the large.
Check:
3(7) + 14(13) =? 203 and 11(7) + 11(13) =? 220
21 + 182 =? 203 and 77 + 143 =? 220
203=203 and 220=220

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