Math for elementary

Question

Your third-grade classroom has 23 boys and girls. Two thirds of the boys and three fourths of the girls are going on a field trip. There are 7 children left. What is the ratio boys to girls in your class

Answer 1

Hi Thalia P.

 

You are given two totals and a couple of fractions, to use to calculate the ratio, if you are into pre-algebra and or getting everything in terms of one variable, I hope you find the substitution process below useful

First let's designate some variables

B = Boys

G = Girls

Now totals

B + G = 23 because there are 23 boys and girls in the classroom.

16 = 23 - 7 = total students who went on a field trip because 7 children were left

According to the information given

(2/3)B + (3/4)G = 16 went on a field trip

Since

B + G = 23

B = 23 - G

For the fractions, I will remove the denominators by multiplying the entire equation by 12

12((2/3)B + (3/4)G = 16)

8B + 9G = 192

Now if we substitute for B in the equation above we can find the number of Girls, G

8(23 - G) + 9G = 192

184 - 8G + 9G = 192

Combine like terms

184 + G = 192

Subtract 184 from both sides of the equation

G = 192 - 184

G = 8

Now we can calculate B

B = 23 - G = 23 - 8 = 15

B = 15

So the ratio of Boys, B to Girls, G is 15 to 8 and this can be checked in the original equation

(2/3)B + (3/4)G = 16

(2/3)*15 + (3/4)*8 = 16

10 + 6 = 16

Answer 2

I used the guess and check method to figure out this problem. First I found possible combinations of boys and girls that would equal 23:

8 boys + 15 girls = 23

9 boys + 14 girls = 23

10 boys + 13 girls = 23

11 boys + 12 girls = 23

12 boys + 11 girls = 23

13 boys + 10 girls = 23

14 boys + 9 girls = 23

15 boys + 8 girls = 23

While compiling this list, I am also looking for a combination of numbers: I need the boy's number to be divisible by 3 (because I need to be able to find 2/3 of them) and I need the girl's number to be equally divisible by 4 (because I need to be able to find 3/4 of them).

15 boys + 8 girls works because I can find 2/3 of 15 (which equals 10) AND 3/4 of 8 (which equals 6).

Now I need to check that there would be exactly 7 children left. So if 10 boys and 6 girls went on the field trip, that is 16 students. If there are 23 total students, then 7 would be left. This checks out.

So that means there are 15 boys and 8 girls in the classroom in all, which is a ratio of 15:8.