# 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? Solution: There is a total reward of$40 given.
Â Let Amelia get = 2x and Mary get = 3x
Then,
2x + 3x = 40
Now, we solve for x
=> 5x = 40
=> x = 8
Thus,
Amelia gets = 2x = 2 Ã— 8 = $16 Mary gets = 3x = 3 Ã— 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?

Solution:

Let the total number of blue marbles be x
Thus,
${\dfrac{3}{4}=\dfrac{x}{120}}$
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.

Solution:

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 Ã— 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.

Solution:

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 Ã— 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.

Solution:

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

Thus,

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

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

=> x = 144

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