Question

there are 42 people in the clas. 3/4 of the boys and 2/3 of the girls travel to school by bus. the total number of biys and girls who travle by bus is 30. How many boys are there in clas? how many girls travel to scool y bus?

Answer 1

24; 12

Explanation:

We can set up a system of equations here.

First we can name the number of boys x,

and the number of girls y.

Now we can set up our equations.

x+y=42

and

3/4x+2/3y=30

Now we can set it up for substitution.

x=42-y

We got that by subtracting y from both sides to the first equation

Now we can substitute 42-y in for x in the second equation.

3/4(42-y)+2/3y=30

Distribute.

31.5-3/4y+2/3y=30

Get a common denominator.

31.5-9/12y+8/12y=30

Combine like terms.

31.5-1/12y=30

Subtract 31.5 from both sides.

-1/12y=-1.5

Multiply both sides by -12

y=18

Now we plug that back in.

x+18=42

Subtract 18 from both sides.

x=24

There are 24 boys in the class.

Now 2/3 of girls use the school bus and the total number of girls is 18.

18*2/3=12

12 girls use the school bus.