Question
Lucy needs to memorize words on a vocabulary list for Latin class. She has memorized 24 of the words, which is three- fourths of the list. How many words are on the list? \( \square \) words
Ask by Chambers Wright. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There are 32 words on the list.
Solution
To determine the total number of words on Lucy's vocabulary list, follow these steps:
1. **Let \( x \) be the total number of words on the list.**
2. **According to the problem, Lucy has memorized 24 words, which is three-fourths of the entire list. This can be expressed as:**
\[
\frac{3}{4}x = 24
\]
3. **To find \( x \), multiply both sides of the equation by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \):**
\[
x = 24 \times \frac{4}{3}
\]
4. **Calculate the multiplication:**
\[
x = 24 \times \frac{4}{3} = 32
\]
5. **Therefore, the total number of words on the list is:**
\[
\boxed{32} \text{ words}
\]
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Simplify this solution Extra Insights
If Lucy has memorized 24 words, which represents three-fourths of the total list, we can find the total number of words by setting up the equation: \( \frac{3}{4} \times x = 24 \), where \( x \) is the total number of words. To find \( x \), we can multiply both sides by \( \frac{4}{3} \): \[ x = 24 \times \frac{4}{3} = 32 \] So, there are 32 words on the list. Let’s break it down a bit more for you: imagine a pizza where Lucy eats three out of every four slices. If she devours 24 slices, the whole pizza must have 32 slices! Remember, multiplying fractions can feel tricky, but it’s just like cutting a pizza—always a delicious problem!
