Word problems in Algebra

Question

A couple does not wish to spend more than $70 for dinner at a restaurant. If a sales tax of 8% is added to the bill and they plan to tip 20% after the tax has been added, what is the most they can spend for the meal? (Round your answer to the nearest cent.)

Answer 1

Let X = how much they will spend to keep the total under $70

then

X+.08X + .20(X+.08X) = 70

1.08X + .2(1.08X) = 70

1.08X + 0.216X = 70

1.296X = 70

X = 70/1.296

X = 54.012

They can't spend more than $54.01

8% tax makes the bill 54.01 x 1.08 = $58.33

add a 20% tip brings the grand total to $69.99

spend one penny more and you go over $70