Questions: A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the after-tax total was 1,585.36, and the tax rate in the area is 6.4%, what was the pre-tax subtotal?

A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the after-tax total was 1,585.36, and the tax rate in the area is 6.4%, what was the pre-tax subtotal?

Transcript text: A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the after-tax total was $\$ 1,585.36$, and the tax rate in the area is $6.4 \%$, what was the pre-tax subtotal? $\$$ $\square$

Solution

Solution Steps

Step 1: Understand the problem

The after-tax total is \$1,585.36, and the tax rate is 6.4%. We need to find the pre-tax subtotal.

Step 2: Set up the equation

Let $ x $ be the pre-tax subtotal. The after-tax total is calculated as: \[ \text{After-tax total} = x + (\text{Tax rate} \cdot x) \] Substitute the known values: \[ 1585.36 = x + (0.064 \cdot x) \]

Step 3: Simplify the equation

Combine like terms: \[ 1585.36 = x(1 + 0.064) \] \[ 1585.36 = 1.064x \]

Step 4: Solve for $ x $

Divide both sides by 1.064 to isolate $ x $: \[ x = \frac{1585.36}{1.064} \] \[ x \approx 1489.98 \]