Six apples and three oranges cost $3.36. Two apples and five oranges cost $3.04. Find the cost of one apple and the cost of an orange.

Question

I need the two equations and the cost of both fruits. I also want to see how you solve it. 

Answer 1

Lets put it this way:

 

Cost of 1 Apple = A

 

Cost of 1 Orange = O

 

 

Six apples and three oranges cost $3.36 equivalent to:

 

6A + 3O = 3.36 (1st equation).

 

Two apples and five oranges cost $3.04 equivalent to:

 

2A + 5O = 3.04 (2nd equation).

 

 

Now we have to solve the 2 equations with 2 uknowns (the cost of 1 Apple = A, and the cost of 1 Orange = O).

 

6A + 3O = 3.36 (Equation 1)

2A + 5O = 3.04 (Equation 2), multiplying this equation by 3 we get:

 

6A + 3O = 3.36 (Equation 1)

6A + 15O = 9.12 (Equation 2), Now equation 2 minus equation 1 we get:

 

 

6A-6A +15O -3O = 9.12-3.36 equivalent to:

 

12O = 5.76 => O = 5.76/12 = 0.48 ( the cost of one Orange is 0.48$)

 

Go back to equation 1 and solve for the cost of 1 apple:

 

6A + 3x0.48 = 3.36 =>

6A + 1.44 = 3.36 =>

6A = 1.92 =>

A = 1.92/6 = 0.32 ( the cost of one apple is 0.32$)

 

Summary: The cost of one apple is 0.32$ and the cost of one orange is 0.48$.

 

Good luck...