Question

Ve fine a variable, set up an equation, and solve. “Three-eighths of the seventh grade students were taking advanced math at the beginning of the year, but seven students dropped out by the end of the year. If there were 140 students taking advanced math at the end of the year, how many total seventh grade students are there?”

Answer 1

Let the total number of seventh grade students be x

Let the number of seventh grade students taking advanced math be k

3/8 of x were taking advanced math at the beginning of the year, i.e

`(3)/(8)\text{ of x}=(3)/(8)* x=(3x)/(8)`

7 students dropped out by the end of the year, i.e

`(3x)/(8)-7=k`

If there were 140 students taking advanced math at the end of the year

`k=140`

Substitute 140 for k into the derived expression to find x

`\begin{gathered} (3x)/(8)-7=k \\ (3x)/(8)-7=140 \\ \text{Collect like terms} \\ (3x)/(8)=140+7 \\ (3x)/(8)=147 \\ \text{Crossmultiply} \\ 3x=147*8 \\ 3x=1176 \\ \text{Divide both sides by 3} \\ (3x)/(3)=(1176)/(3) \\ x=392 \end{gathered}`

Hence, the total number of seventh grade students there is 392