Last modified on August 3rd, 2023

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

Last modified on August 3rd, 2023