Question

Maggie and Tanya went to a fruit store. Maggie bought 10 oranges and 5 apples for $4. Tanya bought 9 oranges and 3 apples for $3. What is the cost of an orange and an apple?​

Answer 1

orange: 0.2$, apple: 0.4$

Explanation:

we mark the price of an orange x and the price of an apple y. then we write down Maggie's and Tanya's purchases as a set of equations:

10 oranges and 5 apples for 4$ means:

`10x + 5y = 4`

9 oranges and 3 apples for 3$ means:

`9x + 3y = 3`

we use the second equation to isolate y:

`3y = 3 - 9x \\ y = 1 - 3x`

and plug it in the first equation:

`10x + 5(1 - 3x) = 4 \\ 10x + 5 - 15x = 4 \\ 1 = 5x \\ x = 0.2`

and then we find y:

`y = 1 - 3 * 0.2 \\ y = 0.4`