Third Lesson (Equal Concept)

Today, we will be learning about the Equal Concept. The word problems in this category explicitly compare two fractions that represent equal quantities. Many a time, these fractions take the form of percentages, decimals or ratios.

Question1 :

James and Jessie had a total of $850. After Jessie spent 1/4 of her money and James spent 1/2 of his money, both had an equal amount of money left. Find the total amount of money each had at first.

Solution1 :

Jessie 1- 1/4= 3/4
James1 - 1/2 = 1/2

3/4 Jessie = 1/2 James
3/4 Jessie = 3/6 James

10 units : $850
1 unit: $85

$85 x 6 =$510#
$85 x 4 = $340#


Question 2 :

Andrew and Ray shared a sum of money. Andrew spent 0.4 of his money and Ray spent 55% of his money. In the end, Ray had thrice as much money as Andrew. Given that Ray had $300 more than Andrew at first, find the amount of money Andrew had at first.

Solution 2:

3x 3/5 Andrew = 9/20 Ray
9/5 Andrew = 9/20 Ray

Difference: 15 units : $300
1 unit : 300 divide 15 = $20

Original amount : 5x 20 =$100#


Question of the day:

A bag contained some red and green marbles. 20% of the red marbles and 0.6 of the green marbles were removed. In the end, there were half as many red marbles as green marbles. Given that there were 30 more green marbles than red marbles at first, find the number of red marbles in the bag at first.

Answer : 10#

This is the end of lesson 3.

Reference from the book "Challenging Maths Problems Made Easy" by Ammiel Wan Chee Hong