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?
Accepted Solution
A:
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.