Kaspar is buying apples and oranges from the market. The total cost of 4 apples and 3 oranges is $11, while the total cost of 2 apples and 5 oranges is $13. What is the cost of each apple and each orange?
Let's assume the cost of each apple is A dollars and the cost of each orange is O dollars.
We can write two equations based on the given information:
4A + 3O = 11 ---(1)
2A + 5O = 13 ---(2)
To solve these equations, we can use the substitution method.
Let's solve equation (1) for A:
4A = 11 - 3O
A = (11 - 3O)/4
Now substitute the value of A in equation (2):
2[(11 - 3O)/4] + 5O = 13
(22 - 6O)/4 + 5O = 13
(22 - 6O) + 20O = 52 (Multiplying both sides by 4 to eliminate the fraction)
22 + 14O = 52
14O = 52 - 22
14O = 30
O = 30/14
O = 15/7
Therefore, the cost of each orange is $15/7 or approximately $2.14.
Now substitute the value of O in equation (1) to find the cost of each apple:
4A + 3(15/7) = 11
4A + 45/7 = 11
4A = 11 - 45/7
28A = 77 - 45
28A = 32
A = 32/28
A = 8/7
Therefore, the cost of each apple is $8/7 or approximately $1.14.
So, the cost of each apple is $1.14 and each orange is $2.14.