6th grade algebra word problem

Question

3/4 of the students in a school were girls and the rest were boys. 2/3 of the girls and 1/2 of the boys attended the school carnival. Find the total number of students in the school if 330 students did not attend the carnival.

Answer 1

First turn the second sentence into an equation. 1/3 of the girls and 1/2 of the boys DIDN'T attend the carnival.

(1/3)g + (1/2)b = 330 --(multiply everything by 6 to get rid of the fractions)--> 2g + 3b = 1980

 

Turn the first sentence into an equation. g + b = total number of students, 3/4 of which are girls

(3/4)(g + b) = g --(multiply everything by 4 to get rid of the fraction)--> 3g + 3b = 4g 

 

Solve the second equation for g by subtracting 3g from both sides

---> g = 3b 

 

Substitute g = 3b into the first equation and solve

--> 2(3b) + 3b = 1980 ---> 9b = 1980 ---> b = 220

 

Substitute b into g = 3b to find g.

---> g = 660

 

The total number of students is g + b so 220 + 660 = 880.

 

Check

660/880 = 3/4 so 3/4 of the students are girls checks

(1/3) of 660 = 220 and (1/2) of 220 = 110. 220 + 110 = 330, the number who did not attend the carnival. So this also checks.

 

I do not know if 6th graders can do this type of algebra, though!