Question

Francine Flicka found a bargain when she bought a lawn mower. She paid the store's clerk three $20 bills and received him $7.45 in change. If the sales tax is 7.3%, what was the selling price of the mower before taxes?

$56.39

$53.55

$52.55

$48.97

Answer 1

$48.97

Explanation:

She paid three $20 bills

3 × 20 = $60

She received $7.45 change

60 - 7.45 = $52.55

The mower was for $52.55 with sales tax.

The sales tax is 7.3%.

Before the sales tax (reduce tax).

52.55 × (1-7.3%)

= $48.97

Answer 2

$48.97

Explanation:

Let p represent the marked price of the mower. Then the price with tax is ...

with tax = p + 7.3%×p = 1.073p

The amount Flicka paid is the amount tendered less the change she received, so is ...

3×$20 - 7.45 = with tax = 1.073p

To find p, we can divide by its coefficient:

(3 × $20 - 7.45)/1.073 = p ≈ $48.97

The selling price before taxes was $48.97.

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Comment on the problem

If you check the answer, you find the amount with tax is ...

$48.97 × 1.073 ≈ $52.54481 ≈ $52.54

so the change Flicka would have received would have been $7.46, not $7.45. If the price were $48.98, then the change would have been $7.44. There is no price at which the mower can be marked that will make the total with tax come to $52.55. There is no solution to this problem.