Solved on Jan 23, 2024

Find the number of boys in a club where there are 25% more girls than boys, and the difference between the number of girls and boys is 36.

STEP 1

Assumptions
1. The number of girls is 25% more than the number of boys.
2. The difference in the number of girls and boys is 36.

STEP 2

Let's denote the number of boys as $b$ . According to the problem, there are 25% more girls than boys.

STEP 3

To express the number of girls, we can write it as $b + 25\% \times b$ .

STEP 4

Convert the percentage to a decimal to make calculations easier.
$25\% = 0.25$

STEP 5

Now, express the number of girls using the decimal form of the percentage.
$\text{Number of girls} = b + 0.25 \times b$

STEP 6

Factor out $b$ to simplify the expression for the number of girls.
$\text{Number of girls} = b(1 + 0.25)$

STEP 7

Calculate the factor within the parentheses.
$1 + 0.25 = 1.25$

STEP 8

Now, we have the expression for the number of girls in terms of $b$ .
$\text{Number of girls} = 1.25b$

STEP 9

According to the problem, the difference between the number of girls and the number of boys is 36.
$\text{Number of girls} - \text{Number of boys} = 36$

STEP 10

Substitute the expression for the number of girls into the equation.
$1.25b - b = 36$

STEP 11

Combine like terms to simplify the equation.
$0.25b = 36$

STEP 12

To find the number of boys, we need to solve for $b$ .
$b = \frac{36}{0.25}$

STEP 13

Calculate the value of $b$ .
$b = \frac{36}{0.25} = 36 \times \frac{1}{0.25}$

STEP 14

Since $\frac{1}{0.25}$ is equivalent to 4, we can multiply 36 by 4.
$b = 36 \times 4$

STEP 15

Calculate the number of boys.
$b = 36 \times 4 = 144$
There are 144 boys in the club.

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Find the number of boys in a club where there are 25% more girls than boys, and the difference between the number of girls and boys is 36.

STEP 1

Assumptions
1. The number of girls is 25% more than the number of boys.
2. The difference in the number of girls and boys is 36.

STEP 2

Let's denote the number of boys as $b$ . According to the problem, there are 25% more girls than boys.

STEP 3

To express the number of girls, we can write it as $b + 25\% \times b$ .

STEP 4

Convert the percentage to a decimal to make calculations easier.
$25\% = 0.25$

STEP 5

Now, express the number of girls using the decimal form of the percentage.
$\text{Number of girls} = b + 0.25 \times b$

STEP 6

Factor out $b$ to simplify the expression for the number of girls.
$\text{Number of girls} = b(1 + 0.25)$

STEP 7

Calculate the factor within the parentheses.
$1 + 0.25 = 1.25$

STEP 8

Now, we have the expression for the number of girls in terms of $b$ .
$\text{Number of girls} = 1.25b$

STEP 9

According to the problem, the difference between the number of girls and the number of boys is 36.
$\text{Number of girls} - \text{Number of boys} = 36$

STEP 10

Substitute the expression for the number of girls into the equation.
$1.25b - b = 36$

STEP 11

Combine like terms to simplify the equation.
$0.25b = 36$

STEP 12

To find the number of boys, we need to solve for $b$ .
$b = \frac{36}{0.25}$

STEP 13

Calculate the value of $b$ .
$b = \frac{36}{0.25} = 36 \times \frac{1}{0.25}$

STEP 14

Since $\frac{1}{0.25}$ is equivalent to 4, we can multiply 36 by 4.
$b = 36 \times 4$

STEP 15

Calculate the number of boys.
$b = 36 \times 4 = 144$
There are 144 boys in the club.

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Find the number of boys in a club where there are 25% more girls than boys, and the difference between the number of girls and boys is 36.

STEP 1

Assumptions1. The number of girls is 25% more than the number of boys.2. The difference in the number of girls and boys is 36.

STEP 2

Let's denote the number of boys as bbb. According to the problem, there are 25% more girls than boys.

STEP 3

To express the number of girls, we can write it as b+25%×bb + 25\% \times bb+25%×b.

STEP 4

Convert the percentage to a decimal to make calculations easier.25%=0.2525\% = 0.2525%=0.25

STEP 5

Now, express the number of girls using the decimal form of the percentage.Number of girls=b+0.25×b\text{Number of girls} = b + 0.25 \times bNumber of girls=b+0.25×b

STEP 6

Factor out bbb to simplify the expression for the number of girls.Number of girls=b(1+0.25)\text{Number of girls} = b(1 + 0.25)Number of girls=b(1+0.25)

STEP 7

Calculate the factor within the parentheses.1+0.25=1.251 + 0.25 = 1.251+0.25=1.25

STEP 8

Now, we have the expression for the number of girls in terms of bbb.Number of girls=1.25b\text{Number of girls} = 1.25bNumber of girls=1.25b

STEP 9

According to the problem, the difference between the number of girls and the number of boys is 36.Number of girls−Number of boys=36\text{Number of girls} - \text{Number of boys} = 36Number of girls−Number of boys=36

STEP 10

Substitute the expression for the number of girls into the equation.1.25b−b=361.25b - b = 361.25b−b=36

STEP 11

Combine like terms to simplify the equation.0.25b=360.25b = 360.25b=36

STEP 12

To find the number of boys, we need to solve for bbb.b=360.25b = \frac{36}{0.25}b=0.2536​

STEP 13

Calculate the value of bbb.b=360.25=36×10.25b = \frac{36}{0.25} = 36 \times \frac{1}{0.25}b=0.2536​=36×0.251​

STEP 14

Since 10.25\frac{1}{0.25}0.251​ is equivalent to 4, we can multiply 36 by 4.b=36×4b = 36 \times 4b=36×4

STEP 15

Calculate the number of boys.b=36×4=144b = 36 \times 4 = 144b=36×4=144There are 144 boys in the club.

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Assumptions
1. The number of girls is 25% more than the number of boys.
2. The difference in the number of girls and boys is 36.

Let's denote the number of boys as $b$ . According to the problem, there are 25% more girls than boys.

To express the number of girls, we can write it as $b + 25\% \times b$ .

Convert the percentage to a decimal to make calculations easier.
$25\% = 0.25$

Now, express the number of girls using the decimal form of the percentage.
$\text{Number of girls} = b + 0.25 \times b$

Factor out $b$ to simplify the expression for the number of girls.
$\text{Number of girls} = b(1 + 0.25)$

Calculate the factor within the parentheses.
$1 + 0.25 = 1.25$

Now, we have the expression for the number of girls in terms of $b$ .
$\text{Number of girls} = 1.25b$

According to the problem, the difference between the number of girls and the number of boys is 36.
$\text{Number of girls} - \text{Number of boys} = 36$

Substitute the expression for the number of girls into the equation.
$1.25b - b = 36$

Combine like terms to simplify the equation.
$0.25b = 36$

To find the number of boys, we need to solve for $b$ .
$b = \frac{36}{0.25}$

Calculate the value of $b$ .
$b = \frac{36}{0.25} = 36 \times \frac{1}{0.25}$

Since $\frac{1}{0.25}$ is equivalent to 4, we can multiply 36 by 4.
$b = 36 \times 4$

Calculate the number of boys.
$b = 36 \times 4 = 144$
There are 144 boys in the club.