Solving Word Problems Involving Ratios
Solving Word Problems Involving Ratios
Word Problems involving ratios are one of the basic applications of Algebra. In this hub, I presented several problems involving ratios. Hope you will find these ones challenging.
Sample Problem Number One :
The ratio of Edward’s money to Gary’s money was 3:2. After spending two hundred pesos each at the internet café, the ratio became 2:1. How much did each have before going to the Internet café ?
Solution :
Let 3X == Edward’s original amount of money
2X == Gary’s original amount of money
Working Equation :
Since each spent two hundred pesos at the Internet café :
(3X – 200)/ (2X – 200) = 2
3X – 200 = 2(2X – 200)
3X – 200 = 4X - 400
400 - 200 = 4X - 3X
X = 200
3(200) = 600 pesos ===èEdward’s original money
2(200) = 400 pesos ==è Gary’s original money
Check : Ratio after each one spent 200 pesos in the Internet cafe
600 – 200 = 400
400 - 200 = 200
400/200 = 2/1
Sample Problem Number Two :
Originally, in Miss Angela Perez special science class, the ratio of boys to girls is 3:4.
From this class, five boys and five girls were eliminated and transferred to regular class. The ratio then of boys to girls becomes 2:3. How many students are there in the original class of Miss Perez ?
Let 3X === Original number of boys
4X === Original number of girls
Working Equation :
According to the problem, five boys and five girls transferred to regular class and the ratio becomes 2:3;
(3X – 5)/(4X – 5) = 2/3
After Cross multiplying we have,
3(3X – 5) = 2(4X – 5)
9X - 15 = 8X - 10
9X – 8X = 15 - 10
X = 5
3(5 ) = 15 == Original number of boys
4(5) = 20 == Original number of girls
Original class size = 15 + 20 = 35
Sample Problem Number Three :
Out of 200 people who joined the pleasure trip to SAMKARA Resort , some were teachers and the rest were students. If 40 students will be added to this group, the ratio of the number of students who joined to the number of teachers present will become 5:1. How many teachers joined this pleasure trip ?
Let X = Number of teachers who joined
200 - X = Number of students who joined
Working Equation :
X/ ( (200 - X) + 40) = 1/5
5X = 200 - X + 40
5X + X = 240
6X = 240
6X/6 = 240/6
X = 40
There were 40 teachers who joined this pleasure trip.
Sample Problem Number Four :
In a certain private hospital, there are 50 attending physicians. This hospital maintains the ratio of the number of patients to the number of doctors as 20:1. How many more doctors should the hospital hire to reduce this ratio to 10:1 ?
Given :
50 = Number of doctors
20 (50) = Number of patients considering the ratio 20:1
Let N = Additional number of doctors to be hired to reduce ratio to 10:1
Working Equation :
(50 + N) / 1000 = 1/10
10(50 + N) = 1000
500 + 10N = 1000
10N = 1000 - 500
10N = 500
10N/10 = 500/10
N = 50
The hospital needs to hire 50 more doctors to reduce the ratio of the numbers of patients to the numbers of doctors to 10:1.
