Last modified on August 3rd, 2023


Ratio Word Problems

Here, we will learn to do some practical word problems involving ratios.

Amelia and Mary share $40 in a ratio of 2:3. How much do they get separately?


There is a total reward of $40 given.
 Let Amelia get = 2x and Mary get = 3x
2x + 3x = 40
Now, we solve for x
=> 5x = 40
=> x = 8
Amelia gets = 2x = 2 × 8 = $16
Mary gets = 3x = 3 × 8 = $24

In a bag of blue and red marbles, the ratio of blue marbles to red marbles is 3:4. If the bag contains 120 green marbles, how many blue marbles are there?


Let the total number of blue marbles be x
x = ${\dfrac{3\times 120}{4}}$
x = 90
So, there are 90 blue marbles in the bag.

Gregory weighs 75.7 kg. If he decreases his weight in the ratio of 5:4, find his reduced weight.


Let the decreased weight of Gregory be = x kg
Thus, 5x = 75.7
x = \dfrac{75\cdot 7}{5} = 15.14
Thus his reduced weight is 4 × 15.14 = 60.56 kg

A recipe requires butter and sugar to be in the ratio of 2:3. If we require 8 cups of butter, find how many cups of sugar are required. Write the equivalent fraction.


Thus, for every 2 cups of butter, we use 3 cups of sugar
Here we are using 8 cups of butter, or 4 times as much
So you need to multiply the amount of sugar by 4
3 × 4 = 12
So, we need to use 12 cups of sugar
Thus, the equivalent fraction is ${\dfrac{2}{3}=\dfrac{8}{12}}$

Jerry has 16 students in his class, of which 10 are girls. Write the ratio of girls to boys in his class. Reduce your answer to its simplest form.


Total number of students = 16
Number of girls = 10
Number of boys = 16 – 10 = 6
Thus the ratio of girls to boys is ${\dfrac{10}{6}=\dfrac{5}{3}}$

A bag containing chocolates is divided into a ratio of 5:7. If the larger part contains 84 chocolates, find the total number of chocolates in the bag.

Let the total number of chocolates be x

Then the two parts are:

${\dfrac{5x}{5+7}}$ and ${\dfrac{7x}{5+7}}$


${\dfrac{7x}{5+7}}$ = 84

=> ${\dfrac{7x}{12}}$ = 84

=> x = 144

Thus, the total number of chocolates that were present in the bag was 144

Last modified on August 3rd, 2023

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