# At a local supermarket Mark can buy 3 oranges and 4 apples for $24 and 2 oranges and 1 apple for $12. How much does each apple and orange cost?

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Let us assume the price of one apple is x and the price of one orange is y.

We have two equations which are to be solved to arrive at x and y.

4x + 3y = 24… (1)

x + 2y = 12 … (2)

We now solve by performing 2*(1) – 3*(2)

=> 2*(4x + 3y) – 3*(x + 2y) = 2*24 – 3*12

=> 8x + 6y – 3x – 6y = 48 – 36

=> 5x = 12

=> x = 2.4

Now substitute x = 2.4 in (1)

=> 4*2.4 + 3y = 24

=> 9.6 + 3y = 24

=> 3y = 14.4

=> y = 4.8

**Therefore one orange costs $4.8 and one apple costs $2.4**

3 oranges and 4 apples cost $24......(1)

2 oranges and one apple cost $12.....(2)

Therefore if we do 4 times the quantity of the purchase at flag (2), we get:

8 oranges and 4 apple =4($12)= $48...(3)

Now compare the purchases at flags (1) and (3) , we get in purchase at flag (3), 8-3 = 5 more oranges for $48 - $24 = $24. So 5 oranges cost $24. Therefore each orange should cost 24/5 dollar = $4.8.

From the purchase at flag (2) we get 2 orange and one apple for cost of $12.

1 Apple should cost $12- cost of 2 oranges = $(12- 2*4.8) = $2.4.

Therefore the price of orange $4.8 and price of apple = $2.4.