Question

1. the regular price of $28 for dog food is discounted by 25%. the sales tax is 8% of the discounted price. the steps used to determine the price of the dog food after the discount is applied including sales tax are shown.

• step 1: $28(\frac{3}{4})(1 + 0.08)$
• step 2: $21(1.08)$
• step 3: $22.68$

which statement is true about the work?
a. an error occurred in step 1 because $\frac{3}{4}$ should have been 0.25.
b. an error occurred in step 1 because $(1 + 0.08)$ should have been 0.92.
c. an error occurred in step 2 because the product of 28 and $\frac{3}{4}$ is $28\frac{3}{4}$.
d. the work is correct and the discounted price of the dog food with sales tax is $22.68.

Explanation:

Step1: Analyze Step 1

A 25% discount means we pay \(100\% - 25\% = 75\%=\frac{3}{4}\) of the original price. The sales tax is 8%, so we multiply by \(1 + 0.08\) to include tax. So Step 1: \(28(\frac{3}{4})(1 + 0.08)\) is correct.

Step2: Analyze Step 2

Calculate \(28\times\frac{3}{4}\): \(28\div4 = 7\), \(7\times3 = 21\). So \(28(\frac{3}{4})=21\), then Step 2: \(21(1.08)\) is correct.

Step3: Analyze Step 3

Calculate \(21\times1.08\): \(21\times1 = 21\), \(21\times0.08 = 1.68\), \(21+1.68 = 22.68\). So Step 3 is correct.

Now check each option:

• Option A: \(\frac{3}{4}\) is correct for 75% (since 1 - 0.25 = 0.75=\(\frac{3}{4}\)), so A is wrong.
• Option B: \(1 + 0.08\) is correct to include 8% tax, so B is wrong.
• Option C: \(28\times\frac{3}{4}=21\), not \(28\frac{3}{4}\), so C is wrong.
• Option D: The work is correct and the final price is $22.68, so D is correct.

Answer:

D. The work is correct and the discounted price of the dog food with sales tax is $22.68.