the 10th - grade class officers ordered t - shirts and sweatshirts to sell as a fundraiser. each t - shirt…

the 10th - grade class officers ordered t - shirts and sweatshirts to sell as a fundraiser. each t - shirt weighed $\frac{1}{2}$ of a pound, and each sweatshirt weighed $\frac{3}{4}$ of a pound. the total weight of the contents of the box was $43\frac{3}{4}$ pounds. which equation written in standard form represents the number of t - shirts, $t$, and the number of sweatshirts, $s$, that were ordered?\n$\frac{1}{2}t+\frac{3}{4}s = 43\frac{3}{4}$\n$\frac{3}{4}s=-\frac{1}{2}s + 43\frac{3}{4}$\n$2t + 3s=175$\n$3s=-2t + 175$

the 10th - grade class officers ordered t - shirts and sweatshirts to sell as a fundraiser. each t - shirt weighed $\frac{1}{2}$ of a pound, and each sweatshirt weighed $\frac{3}{4}$ of a pound. the total weight of the contents of the box was $43\frac{3}{4}$ pounds. which equation written in standard form represents the number of t - shirts, $t$, and the number of sweatshirts, $s$, that were ordered?\n$\frac{1}{2}t+\frac{3}{4}s = 43\frac{3}{4}$\n$\frac{3}{4}s=-\frac{1}{2}s + 43\frac{3}{4}$\n$2t + 3s=175$\n$3s=-2t + 175$

Answer

Answer:

C. $2t + 3s = 175$

Explanation:

Step1: Write the initial equation

The weight of t - shirts is $\frac{1}{2}t$ (since each t - shirt weighs $\frac{1}{2}$ pound and there are $t$ t - shirts) and the weight of sweatshirts is $\frac{3}{4}s$ (since each sweatshirt weighs $\frac{3}{4}$ pound and there are $s$ sweatshirts), and the total weight is $43\frac{3}{4}=\frac{43\times4 + 3}{4}=\frac{172+3}{4}=\frac{175}{4}$ pounds. So the equation is $\frac{1}{2}t+\frac{3}{4}s=\frac{175}{4}$.

Step2: Clear the fractions

Multiply each term in the equation $\frac{1}{2}t+\frac{3}{4}s=\frac{175}{4}$ by 4 to get rid of the denominators. We have $4\times\frac{1}{2}t+4\times\frac{3}{4}s = 4\times\frac{175}{4}$.

Step3: Simplify the equation

$2t + 3s=175$. This is the standard - form equation ($Ax + By = C$, where $A = 2$, $B = 3$, and $C = 175$).