CBSE Class 8 Mathematics Linear Equations in One Variable Notes Set 09

Steps for Solving Word Problems

Read the statement twice and name the unknown (for example, let the number be x). Write each condition as an equation, solve it, and finally substitute your value back in the original words to be sure it works.

Typical Set-ups

Consecutive numbers: x, x + 1, x + 2 (integers); x, x + 2, x + 4 (even or odd numbers); multiples of 8: 8n, 8(n + 1), 8(n + 2).
Digits: a two-digit number with tens digit a and units digit b equals 10a + b; reversed it is 10b + a.
Ratios: a ratio p : q means the numbers are px and qx.
Ages: if the present age is x, the age n years later is x + n and n years ago is x - n. Keep the age difference of two people constant.
Coins and notes: total value = sum of (number of pieces x value of each).
Fractions: let the fraction be x/y and form two equations from the changes made to the numerator and denominator.

Equations with the Variable in the Denominator

If the equation has the form (ax + b)/(cx + d) = p/q, cross-multiply to get q(ax + b) = p(cx + d) and solve the linear equation. The value must not make any denominator zero.

Worked example: z/(z + 15) = 4/9. Cross-multiplying, 9z = 4z + 60, so 5z = 60 and z = 12. Check: 12/27 = 4/9.

Worked example: a number is as much greater than 36 as 86 is greater than it. Then x - 36 = 86 - x, so x = 61.