Question

Think About the Process  You have 50 quarters. You find 20​% more quarters in your room. Then you go shopping and spend 75​% of the total number of quarters. Write an expression to represent the total number of quarters you take with you shopping.​ Calculate, in​ dollars, the amount of money you have left.
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Part 1
What expression represents your total number of​ quarters?
A.50 plus left parenthesis 50 divided by 0.75 right parenthesis
50 plus left parenthesis 50 divided by 0.75 right parenthesis
B.50 plus left parenthesis 50 times 0.20 right parenthesis
50 plus left parenthesis 50 times 0.20 right parenthesis
C.50 plus left parenthesis 50 divided by 20 right parenthesis
50 plus left parenthesis 50 divided by 20 right parenthesis
D.50 plus left parenthesis 50 times 20 right parenthesis
50 plus left parenthesis 50 times 20 right parenthesis

Answer 1

To find the total number of quarters you take shopping after finding 20% more quarters, we can break this down step by step.

1. **Current Number of Quarters**: You start with 50 quarters.
2. **Finding 20% More Quarters**: To calculate 20% of 50:
\[
20\% \text{ of } 50 = 0.20 \times 50 = 10
\]
So, you find 10 additional quarters.
3. **Total Number of Quarters**: Now, add these additional quarters to the original number:
\[
\text{Total} = 50 + 10 = 60
\]

Now we can address the options to represent the total number of quarters:

- A. \(50 + \frac{50}{0.75}\) This expression doesn't correctly represent finding 20% more.
- B. \(50 + (50 \times 0.20)\) This expression correctly represents the total number of quarters since \(50 \times 0.20 = 10\) more quarters making a total of \(60\).
- C. \(50 + \frac{50}{20}\) This would incorrectly calculate and doesn't relate to adding 20%.
- D. \(50 + (50 \times 20)\) This would add a much larger number and is incorrect.

Thus, the correct expression representing your total number of quarters is:

**Answer: B. \(50 + (50 \times 0.20)\)**

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Now, let’s calculate how much money you have left after spending 75% of the total number of quarters.

1. **Total Quarters**: 60
2. **Spending 75% of Quarters**:
\[
75\% \text{ of } 60 = 0.75 \times 60 = 45
\]
3. **Quarters Left**:
\[
60 - 45 = 15
\]

4. **Amount in Dollars**: Since each quarter is worth $0.25, the total amount of money left in dollars will be:
\[
15 \times 0.25 = 3.75
\]

Thus, the amount of money you have left after shopping is **$3.75**.