Posted by Jane on Wednesday, January 4, 2012 at 5:56pm.
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?

math  Reiny, Wednesday, January 4, 2012 at 7:56pm
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
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