n Mrs Hoffmans fifthgrade class 49 of the students are boys

n Mrs. Hoffman’s fifth-grade class 4/9 of the students are boys. To make the number of boys and girls equal, 2 girls go to the other fifth grade class and 2 boys come from that class to Mrs. Hoffman’s class. How many students are in Mrs. Hoffman’s class now?

Use algebra to solve the problem. Solutions involving trial-and-error will not earn any credit. Please define your variables and write the equation you used as a part of the solution.

Here is a similar problem:

In Mrs. Hoffman’s fifth-grade class 2/3 of the students are boys. To make the number of boys and girls equal, 4 boys go to the other fifth grade class and 4 girls come from that class to Mrs. Hoffman’s class. How many students are in Mrs. Hoffman’s class now?

Defining the variable:

Original #’s

New #

Boys

2x

2x-4

Girls

x

x+4

Setting up the equation:

2x-4 = x+4

Solving the equation:

2x-4 = x+4

Þ 2x – x = 4+4

Þ x = 8

Ans: The numbers students in Mrs. Hoffman’s class now 24.

Solution

Defining the variable:

Original #’s

New #

Boys

4x

4x + 2

Girls

5x

5x - 2

Setting up the equation:

2x-4 = x+4

Solving the equation:

4x + 2 = 5x - 2

=> 5x – 4x = 2 + 2

=> x = 4

Hence , the number of students in Mrs. Hoffman’s class now is

4x + 5x = 4(4) + 5(4) = 16 + 20 = 36