Question

Lauren and Lisa are selling apples and oranges to raise money for their trip to Southern California. Lauren sells 3 boxes of apples and 14 boxes of oranges for a total of $203. Lisa sold 11 boxes of oranges and 11 boxes of apples for $220. How much would it cost for 2 boxes of apples and 3 boxes of oranges

Answer 1

Lauren and Lisa's sales can be represented as a system of linear equations. Using elimination, we find the cost of one box of apples to be $7 and one box of oranges to be $13. Hence, 2 boxes of apples and 3 boxes of oranges cost $53.

Step-by-step explanation:

We have a system of linear equations here where we need to find the cost of one box of apples and one box of oranges. Let x represent the cost of one box of apples and y represent the cost of one box of oranges. From the problem, we have two equations:

1. 3x + 14y = $203 (Lauren's sales)
2. 11x + 11y = $220 (Lisa's sales)

To solve for x and y, we need to use the method of substitution or elimination. Let's use elimination:

1. Multiply the first equation by 11 and the second equation by 3:
2. 33x + 154y = 2233
3. 33x + 33y = 660
4. Subtract the second equation from the first:
5. 121y = 1573
6. Divide by 121 to find y:
7. y = $13 (cost of one box of oranges)
8. Now plug the value of y back into one of the original equations to find x:
9. 3x + 14(13) = 203
10. 3x + 182 = 203
11. 3x = 21
12. X = $7 (cost of one box of apples)

Finally, to find the cost for 2 boxes of apples and 3 boxes of oranges:

1. 2x + 3y = 2(7) + 3(13)
2. $14 + $39 = $53

Therefore, 2 boxes of apples and 3 boxes of oranges will cost $53.