At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 5 items that each cost the same amount, but each was $1.50 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.

Answer:Part a) [tex]3x=5(x-1.50)[/tex]Part b) [tex]x=\$3.75[/tex]Part c) see the explanation in Part c)Part d) see the explanation in Part d)Step-by-step explanation:Part a) Write an equationLetx -----> represent the cost of one of Tanya's itemsy ----> represent the cost of one of Tony's itemswe know that[tex]y=x-1.50[/tex]Tanya bought 3 items -----> 3xTony bought 5 items -----> 5y----> 5(x-1.50) If Tanya and Tony paid the same amount of moneythen The cost of three of Tanya's items is equal to the the cost of five of Tony's itemsso[tex]3x=5(x-1.50)[/tex]Part b) Solve the equationwe have[tex]3x=5(x-1.50)[/tex]Solve for xdistribute the right side[tex]3x=5x-7.50[/tex]Group terms that contain the same variable[tex]5x-3x=7.50[/tex]Combine like terms'[tex]2x=7.50[/tex]Divide by 2 both sides[tex]x=\$3.75[/tex]Find the value of y[tex]y=3.75-1.50=\$2.25[/tex]Part c) Check your solutionsubstitute the value of x in the originally equation[tex]3(3.75)=5(3.75-1.50)[/tex][tex]11.25=5(2.25)[/tex][tex]11.25=11.25[/tex] ----> is verifiedPart d) State the solution in complete sentenceswe have thatThe cost of one of Tanya's items was $3.75Tanya paid $11.25 for 3 itemsThe cost of one of Tony's items was $2.25Tony paid $11.25 for 5 itemsTanya and Tony paid the same amount of money