+-2 3. 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. Show your work. (c) Check your solution. Show your work. (d) State the solution in complete sentences.
Let x represent the cost of one of Tanya's items.
Then the cost of one of Tony's items =x - 2.25. But we have:
3x =4(x - 2.25)
3x =4x - 9 subtract 3x from both sides
0 =x - 9 add 9 to both sides
x=$9 The cost of one of Tanya's items
$9 x 3 =$27 Total cost of Tanya's 3 items
$9 - $2.25 =$6.75 cost of one of Tony's items.
$6.75 x 4 =$27 Total cost of Tony's 4 items.
3 x $9 =4 x $6.75 =$27. This shows that both Tony and Tanya spent the same amount of money.
