Two numbers a and b are in the ratio 3:2. If both numbers are increased by 2, the ratio of resulting numbers becomes 5:4, find a and b

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter2: Linear Equations
Section2.6: Ratios And Proportions
Problem 58PFA
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Two numbers a and b are in the ratio 3:2. If both numbers are increased by 2, the ratio of resulting numbers becomes 5:4, find a and b

Expert Solution
Step 1

We are given a:b = 3:2 ....(i)

If a and b is increased by 2 that is (a+2) and (b+2)

Then, 

(a+2):(b+2) = 5:4...(ii)

 

Step 2

From equation (i) in Step 1

a = 3x , b = 2x for some number variable x

Then plug this in equation (ii)

=> (3x+2):(2x+2) = 5:4

=> (3x+2)/(2x+2) = 5/4

=> 4(3x+2) = 5(2x+2)

=> 12x+8 = 10x+10

=> 12x-10x = 10-8

=> 2x = 2

=> x = 1

Hence a = 3(1) = 3, b = 2(1) = 2

Therefore the numbers a and b are 3 and 2 

 

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