Question

The cost of 10 oranges and 3 apples is $2.77. Twenty four oranges and 12 apples cost $8.04. How do you find cost of each orange and apple?

Answer 1

An apple costs `0.29`$, while an orange costs `0.19`$.

Explanation:

Let's call `a` the price of an apple and `o` the price of an orange.

From the first relation, we know that

`10o +3a=2.77`

From the second, we know that

`24 o + 12 a =8.04`

Now, there are several ways to solve this system: for example, we can multiply by `4` the first equation to get

`10o +3a=2.77 -> 40o + 12a = 11.08`

Now, subtracting the second equation from the first, we get

`40o + 12 a - 24o - 12a = 11.08-8.04`, which means

`16o = 3.04`, from which we get `o=3.04/16=0.19`

Once we know the price of an orange, we can easily get the price of an apple by sostituition: for example, from the first equation we know that

`10o +3a=2.77`

but now we know that an orange costs `0.19`, so this equation becomes

`1.9+3a=2.77`, from which we get

`a={2.77-1.9}/3=0.29`