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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 -

    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

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