Find the cost of each orange and each apple.

Question

The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68.

Answer 1

Hi Jake,

 

First, pick variables to represent the unknowns.

 

Let c = cost of oranges

Let a = cost of apples

 

Note: you can call your variables whatever you wish.  I normally

try to use variables that I can immediately identify... a for apple,

f for father, K for Kyra, ... and so forth.  In this case, o for orange

is confusing due to similarity to 0.  I chose c for citrus just because.

If you are more comfortable with x, y that's fine.

 

12c + 7a = 5.36   {equation 1}

8c + 5a = 3.68     {equation 2}

 

Let's solve by elimination.  Multiply equation 1 by 2

and multiply equation 2 by -3.  Then add equations

to eliminate the c variable and solve for a.

 

 24c + 14a = 10.72

-24c - 15a = -11.04

----------------------------

             -a = -0.32

 

apples cost $0.32

 

Plug 0.32 in for the value of a in either of the original equations

and solve for c to find the cost of an orange.