In the previous two posts, we have learned how to solve word problems involving ratio with two and three quantities. In posts, we are going to learn how to solve a slightly different problem where both numbers are increased.
The ratio of two numbers is 3:5 and their sum is 48. What must be added to both numbers so that the ratio becomes 3:4?
Solution and Explanation
First, let us solve the first sentence. We need to find the two numbers whose ratio is 3:5 and whose sum is 48.
Now, let x be the number of sets of 3 and 5.
3x + 5x = 48
8x = 48
x = 6
Now, this means that the numbers are 3(6) = 18 and 5(6) = 30.
Now if the same number is added to both numbers, then the ratio becomes 3:4.
Recall that in the previous posts, we have discussed that ratio can also be represented by fraction. So, we can represent 18:30 as . Now, if we add the same number to both numbers (the numerator and the denominator), we get . If we let that number y, then
Cross multiplying, we have
By the distributive property,
So, we add 18 to both the numerator and denominator of . That is,
Now, to check, is ? Yes, it is. Divide both the numerator and the denominator by 12 to reduce the fraction to lowest terms.