Question

Well he buys two books at a bookstore. He spent $44.52 after 6% sales tax is applied, but the clerk does not provide him with the receipt. He knows that book A cost $17.50 before sales tax , But he is not sure how much book B costs.

A. Use an arithmetic solution to find the cost of book B.

B. Determine how much the cost of book B can be represented in an equation. Write an equation using the distributive property that represents this situation.

C. Use the equation from part b to find the cost of book B. Show your work.

D. Explain how finding the cost of book B using the arithmetic solution compares to finding the cost of book B using the algebraic solution.

Answer 1

Let x represent the cost of book B

Book A: $17.50

Book B: x

Sales tax: (A + B) x 6% = .06(17.50 + x) = 1.05 + .06x

book A + book B + sales tax = total cost

(17.50) + (x) + (1.05 + .06x) = 44.52 plugged in all of the values

18.55 + 1.06x = 44.52 added like terms

1.06x = 25.97 subtracted 18.55 from both sides

x = 24.50 divided 1.06 from both sides

Answer: $24.50