Question

At a bargain store, Lisa bought 2 shirts that each cost the same amount. Dave bought 4 shorts that each cost the same amount, but each was $3.50 less than the shirts that Lisa bought. Both Lisa and Dave paid the same amount of money. What was the individual cost of each person's items?
a) Write an equation. Let x represent the cost of one of Lisa's items. (4 points)
b) Solve the equation. Show your work. (5 points)
c) Check your solution. Show your work. (5 points)
d) State the solution in complete sentences. (1 point)

Answer 1

a) The total cost of Lisa's purchase was 2x. The individual cost of Dave's purchase was (x-3.50), so his total cost was 4(x-3.50). These costs were equal, so an approriate equation is

... 2x = 4(x -3.50)

b) Eliminate parentheses, subtract 2x, divide by 2.

... 2x = 4x -14.00

... 0 = 2x -14.00

... 0 = x - 7.00

Add 7 to show the value of x

... 7.00 = x

c) Lisa's total purchase was 2x = 14.00. Dave's items cost 7.00 -3.50 = 3.50 each, and the 4 of them came to 4×$3.50 = $14.00, the same as Lisa's total.

d) The cost of one of Lisa's shirts was $7.00; the cost of one of Daves shorts was $3.50.