Question

5 apples and 3 oranges cost $3.50 and 4 apples and 5 oranges cost $4.10. How much does one apple and one orange cost.

Let x = the cost of one apple.

Let y = the cost of one orange.

a. Write an equation for the cost of 5 apples plus 3 oranges.
b. Write an equation for the cost of 4 apples plus 5 oranges.
c. Solve the above system of equations using multiplication.
d. What is the cost of one apple? What is the cost of one orange?

Answer 1

Let x= cost of apple and y= cost of orange:
5x+3y=3.50, 4x+5y=4.10.
So 20x+12y=14, so 20x=14-12y; 20x+25y=20.50.
Substitute for 20x in the second equation: 14-12y+25y=20.50
13y=6.50, y=0.50. But 5x=3.50-3y, so 5x=3.50-1.50=2.00 and x=0.40.
Therefore the cost of one apple is 40 cents and one orange is 50 cents.

Answer 2

x= cost of apple and y= cost of orange:

5x+3y=3.50, 4x+5y=4.10.

So 20x+12y=14, so 20x=14-12y; 20x+25y=20.50.

Substitute for 20x in the second equation: 14-12y+25y=20.50

13y=6.50, y=0.50. But 5x=3.50-3y, so 5x=3.50-1.50=2.00 and x=0.40.

so the cost of one apple is 40 cents and one orange is frickiin 50

Explanation: