Question

In Algebra High School, 20 students are taking Mandarin this year. This number has been increasing at a rate of 4 students per year. The number of students taking French is 12. This number has been decreasing at a rate of 5 students per year. At these rates, when will the number of students taking Mandarin equal the number taking French? Write and solve an equation to answer the question.

Answer 1

The number of students taking Mandarin will never equal the number taking French.

Step-by-step explanation:

To determine when the number of students taking Mandarin will equal the number taking French, we need to set up an equation using the given information.

Let 'y' represent the number of years.

The equation for the number of students taking Mandarin is 20 + 4y, and the equation for the number of students taking French is 12 - 5y.

To find when these numbers are equal, we set up the equation:

20 + 4y = 12 - 5y.

Next, we solve the equation:

20 + 4y = 12 - 5y

Combine like terms:

9y = -8

Divide by 9:

y = -8/9

The number of years cannot be negative, so there is no solution to this equation. Therefore, the number of students taking Mandarin will never equal the number taking French under the given conditions.