Mathematics
Grade10
Easy

Question

The ratio of incomes of two persons is 9:7, and the ratio of their expenditure is 4:3. If each of them manages to save $2000 per month, find their monthly expenditure?

  1. $16000, $12000
  2. $8000, $10000
  3. $11000, $20000     
  4. None of the above

hintHint:

An equation with the maximum order of 1 and an equation of a straight line is called the linear equation. 

The correct answer is: $16000, $12000


    Step 1 of 1:
    We have given the ratio of incomes of two persons is 9:7, and the ratio of their expenditure is 4:3. If each of them manages to save $2000 per month
    Let the income be x and expenditure be y
    Saving per month = $2000
    Then
    9x – 4y = 2000………………….. 1
    7x – 3y = 2000……………… 2
    From 1
    9x – 4y = 2000
    9x = 2000 + 4y
    x = fraction numerator 2000 plus 4 y over denominator 9 end fraction
    Substituting x in 2nd equation,
    open parentheses fraction numerator 2000 plus 4 y over denominator 9 end fraction close parentheses  - 3y = 2000
    fraction numerator 14000 plus 28 y over denominator 9 end fraction - 3y = 2000
    14000+ 28y – 27y = 18000
    14000 + 1y = 18000
    y = 4000
    4y = 4 x 4000
    =16000
    3y = 3 x 4000
    = 12000

    The substitution method is the algebraic method to solve simultaneous linear equations

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