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

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 7:56pmlet 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

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