Question

At Sunnyside High School, 100 students are taking French, and this number is decreasing at a rate of 2 students per year. The number of students taking Spanish is 75 and is increasing at a rate of 7 students per year. At these rates, when will the number of students taking French equal the number of students taking Spanish?

A. 1 year
B. 2 years
C. 4 years
D. 10 years

Answer 1

It will take approximately 2.77 years (or 2 years and 9 months) for the number of students taking French to equal the number of students taking Spanish.

Step-by-step explanation:

To find when the number of students taking French will equal the number of students taking Spanish, we need to set up and solve an equation. Let x represent the number of years. The number of students taking French can be represented by the equation 100 - 2x, and the number of students taking Spanish can be represented by the equation 75 + 7x. We can set these two expressions equal to each other:

100 - 2x = 75 + 7x

Combine like terms:

100 - 75 = 7x + 2x

25 = 9x

Divide both sides by 9:

x = 25/9

So, it will take approximately 2.77 years (or 2 years and 9 months) for the number of students taking French to equal the number of students taking Spanish. Therefore, the answer is B. 2 years.