Question
The 10th-grade class officers ordered t-shirts and sweatshirts to sell as a fundraiser. Each t-shirt weighed StartFraction one-half EndFraction. of a pound, and each sweatshirt weighed StartFraction 3 Over 4 EndFraction of a pound. The total weight of the contents of the box was 43 and StartFraction 3 Over 4 EndFraction pounds. Which equation written in standard form represents the number of t-shirts, t, and the number of sweatshirts, s, that were ordered?
StartFraction one-half EndFraction t plus StartFraction 3 Over 4 EndFraction s equals 43 and StartFraction 3 Over 4 EndFraction
StartFraction 3 Over 4 EndFraction s equals negative StartFraction one-half EndFraction s plus 43 and StartFraction 3 Over 4 EndFraction.
2t + 3s = 175
3s = –2t + 175
StartFraction one-half EndFraction t plus StartFraction 3 Over 4 EndFraction s equals 43 and StartFraction 3 Over 4 EndFraction
StartFraction 3 Over 4 EndFraction s equals negative StartFraction one-half EndFraction s plus 43 and StartFraction 3 Over 4 EndFraction.
2t + 3s = 175
3s = –2t + 175
Answers
GPT-4o mini
To solve the problem, we first need to convert the total weight of the contents of the box from a mixed number to an improper fraction or a decimal for easier calculations.
The total weight given is \( 43 \frac{3}{4} \) pounds. We can convert this to an improper fraction:
\[
43 \frac{3}{4} = 43 + \frac{3}{4} = \frac{43 \times 4}{4} + \frac{3}{4} = \frac{172}{4} + \frac{3}{4} = \frac{172 + 3}{4} = \frac{175}{4}
\]
Now, we can express the weight of the t-shirts and sweatshirts in terms of their respective weights:
- Each t-shirt weighs \( \frac{1}{2} \) pound.
- Each sweatshirt weighs \( \frac{3}{4} \) pound.
Now, we can write the equation for the total weight of the t-shirts and sweatshirts:
\[
\frac{1}{2}t + \frac{3}{4}s = \frac{175}{4}
\]
To eliminate the fractions, we can multiply the entire equation by 4:
\[
4 \left(\frac{1}{2}t\right) + 4 \left(\frac{3}{4}s\right) = 4 \left(\frac{175}{4}\right)
\]
This simplifies to:
\[
2t + 3s = 175
\]
Now we can see that \( 2t + 3s = 175 \) is indeed the standard form of the equation representing the number of t-shirts, \( t \), and the number of sweatshirts, \( s \) that were ordered.
Thus, the correct equation in standard form is:
\[
2t + 3s = 175
\]
The total weight given is \( 43 \frac{3}{4} \) pounds. We can convert this to an improper fraction:
\[
43 \frac{3}{4} = 43 + \frac{3}{4} = \frac{43 \times 4}{4} + \frac{3}{4} = \frac{172}{4} + \frac{3}{4} = \frac{172 + 3}{4} = \frac{175}{4}
\]
Now, we can express the weight of the t-shirts and sweatshirts in terms of their respective weights:
- Each t-shirt weighs \( \frac{1}{2} \) pound.
- Each sweatshirt weighs \( \frac{3}{4} \) pound.
Now, we can write the equation for the total weight of the t-shirts and sweatshirts:
\[
\frac{1}{2}t + \frac{3}{4}s = \frac{175}{4}
\]
To eliminate the fractions, we can multiply the entire equation by 4:
\[
4 \left(\frac{1}{2}t\right) + 4 \left(\frac{3}{4}s\right) = 4 \left(\frac{175}{4}\right)
\]
This simplifies to:
\[
2t + 3s = 175
\]
Now we can see that \( 2t + 3s = 175 \) is indeed the standard form of the equation representing the number of t-shirts, \( t \), and the number of sweatshirts, \( s \) that were ordered.
Thus, the correct equation in standard form is:
\[
2t + 3s = 175
\]