math
posted by Jane .
Please explain in detail how to solve each 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?

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 = 350x
also x:y = 33:37
x/y = 33/37
37x = 33y
37x = 33(350x)
37x = 11550  33x
70x = 11500
x = 165
then y = 350165 = 185
as I found much easier and faster above