Please explain in detail how to solve each question:

Question

At a certain high school, 350 students are taking an algebra course. The ratio of boys to girls taking algebra is 33:37. How many more girls are taking algebra than boys?

How can you write a system of equations to model the situation?

Which equation will you solve for a variable in the firs step of solving the system? Why?

How can you interpret the solution in the context of the problem?

Answer 1

let the number of boys be 33x and the number of girls be 37x
(notice 33x : 37x = 33:37 )

33x + 37x = 350
70x = 350
x = 5

so number of boys = 33(5) = 165
number of girls = 37(5) = 185
So 20 more girls than boys take algebra

check:
notice 165+185 = 350
and 165:185 = 33:37

No need to have a system of equations here, the above is the simplest way to do ratio problems.

I suppose you could say
number of boys -- x
number of girls -- y
then x+y = 350 , or y = 350-x

also x:y = 33:37
x/y = 33/37
37x = 33y
37x = 33(350-x)
37x = 11550 - 33x
70x = 11500
x = 165
then y = 350-165 = 185
as I found much easier and faster above

Answer 2

Wow

Uh my tiny 8th grade mind needed to read that twice... heh... I'm slow.

Answer 3

I am so confused, I need more help please!!!