Word Problem Solving Example 2

Question:
Tom ears ten percent more than Kavin. Kavin earns three-fifth of what John earns. What percent of John's earning is Tom's?
Solution:
let T be Tom's salary, K be Kavin's salary and J be John's salary.
The first statement is: Tom ears 10% more than Kevin,
translate it into a mathematics expression:
T = K + (10/100)K = K(1 + 10/100) = K(1 + 1/10) = K(10/10 + 1/10) = (11/10)K, this is our equation(1).
The second statement is: Kevin earns three-fifth of what John earns,
translate it into a mathematics expressiom:
K = (3/5)J, this is our equation(2).
The question ask for: what percent of John's earning is Tom's?
Thanslate it into a mathematics expression:
T/J = ?
Now let us to solve this problem.
The first equation is: T = (11/10)K.
The second equation is: K = (3/5)J.
From the second equation, express J in terms of K: J = 5K/3,
then T/J = 11K/10 ÷ 5K/3 = 11K/10 × (3)/(5K),
both numerator and denominator divide by K and the variable K is removed.
then T/J = 11/10 × 3/5 = 33/50 = 66/100
So T = (66/100)J
That is, Tom's salary is 66% John's salary.

The problem and solving in this section are for students in grad 6, 7 and 8. Translate word language into a mathematics expression by finding relationship between different objects, write equation based on the relationship and solve equations to find the values of the different objects. This practice can train our brain to obtain the logic thinking skill.