Finding the total amount given the percentage of a partial amount

In this lesson, we solve problems where we find the total amount given the partial amount and the percentage. Words in problems like ‘altogether’, ‘entire’, ‘in all’, ‘whole’ mean the total.

We solve such problems using a proportion. A proportion, as we have learnt, is an equality of two ratios.

$$\frac{percent}{100} = \frac{partial \: amount}{total \: amount(x)}$$

The total amount is the unknown quantity (x) that we need to find.

Percent and the partial amount are given and are known quantities

Cross multiplying and solving for x, gives the value of the total amount.

$$\frac{percent}{100} = \frac{partial \: amount}{total \: amount(x)}$$

$$Total \: amount = \frac{partial \: amount}{percent} \times 100$$

Formula

$$Total = \frac{part}{percent} \times 100$$

Consider the following solved examples.

Your friend has a bag of marbles and he tells you that 20% of the marbles are red. If they are 7 red marbles. How many marbles does he have altogether?

Solution

Step 1:

Number of red marbles = 7

Percentage of red marbles = 20%

Step 2:

Using formula

$Total = \frac{part}{percent} \times 100$

The total number of marbles $\frac{7}{20} \times 100 = 35$

A high school marching band has 12 flute players. If 8% of the band members play the flute, then how many members are in the entire band?

Solution

Step 1:

Number of flute players = 12

Percentage of flute players = 8%

Step 2:

Using formula

$Total = \frac{part}{percent} \times 100$

Total number of flute players $\frac{12}{8} \times 100 = 150$

A small school has 60% boys and rest girls. If the number of boys is 48, what is the total number of boys and girls altogether in the school?

Solution

Step 1:

Percentage of the boys in school = 60%

Number of boys in the school = 48

Step 2:

Using formula

$Total = \frac{part}{percent} \times 100$

Total number of students $\frac{48}{60} \times 100 = 80$