Question

in the sophomore class at Summit High School the number of students taking French is 2/3 of the number taking Spanish. how many students are studying each language if the total number of students in French and Spanish is 310 ?This is Homework

Answer 1

From the information given in the statement let be

`\begin{gathered} f=(2)/(3)s\text{ (1)} \\ f+s=310\text{ (2)} \end{gathered}`

Where

*f: number of students taking a French class

*s: number of students taking a Spanish class

So, you have a system of linear equations, which you can use the substitution method.

To do this, replace the value of the first equation in the second equation and solve for s

`\begin{gathered} f+s=310\text{ (2)} \\ (2)/(3)s+s=310 \\ (5)/(3)s=310 \\ \text{ Multiply by }(3)/(5)\text{ on both sides of the equation} \\ (3)/(5)\cdot(5)/(3)s=310\cdot(3)/(5) \\ s=186 \end{gathered}`

Now,