Question

At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 4 items that each cost the same amount, but each was $2.25 less than the items that Tanya bought. Both Tanya and Tony 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 Tanya's items.
(b) Solve the equation.
(c) Check your solution.
(d) State the solution in complete sentences.

How would I write an equation for part (a)?

Answer 1

If Tanya’s three items (x) cost the same as Tony’s four items (y), 3x = 4y. Y is 2.25 less than x, so: 3x = 4x - 4 x 2.25. 3x = 4x - 9. 3x + 9 = 4x. 9 = x. Therefore, y = 9 - 2.25. x = 9 and y = 6.75. Three times 9 and four times 6.75 is 27. Tanya’s items cost $9 each and Tony’s cost $6.75.