What is the cost for one of each fruit?

Question

An apple costs the same as 2 oranges. Together, an orange and a banana cost $.10 more than an apple. Two oranges cost $.15 more than a banana.

Answer 1

An apple costs the same as 2 oranges. Together, an orange and a banana cost $.10 more than an apple. Two oranges cost $.15 more than a banana.

 

x = apples

y = oranges

z = bananas

 

x = 2y                 {equation 1}

y + z = x + 10     {equation 2}

2y = z + 15         {equation 3}

 

Using substitution of 2y in place of x in equation 2

y + z = 2y + 10

 

From equation 3, z = 2y - 15

Substitute that into previous

 

y + 2y - 15 = 2y + 10

3y - 15 = 2y + 10

subtract 2y and add 15 to both sides

y = 25

 

x = 2y = 50

 

z = 2y - 15 = 85

 

apples cost $.50, oranges cost $.25, bananas cost $.85