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?

1 Answer
Sep 23, 2015

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