32 students, 9 left, 3/4 girls, 2/3 boys, ratio of boys to girls

Question

There are 32 students in your classom, 2/3 of the boys are going on a fieldtrip and 3/4 of the girls are going as well. There are 9 students left, what is the ratio of boys to girls?

Answer 1

Let B=number of boys and G=number of girls, B+G=32, so B=32-G.

2B/3+3G/4+9=32, 2B/3+3G/4=23, 2(32-G)/3+3G/4=23.

Multiply through by 12: 8(32-G)+9G=276.

256-8G+9G=276, G=276-256=20 so B=12.

Ratio boys:girls=12:20=3:5.

Comments

Algebra is probably the easiest way to solve the problem. You can solve it graphically by drawing two lines y=32-x and ⅔x+¾y=23. Where the lines intersect gives x and y where x represents the number of boys and y the number of girls. To make it easier you can multiply the second equation by 12 to get rid of the fractions: 8x+9y=276, so y=(276-8x)/9. You use the intersection point to find x and y then you can work out the ratio. Remember that to draw a line graph you only need two points to join together, usually the x and y intercepts (solving for y=0 and x=0).