Determine the ratio of boys and girls

[burgess]

Help me to solve algebra 1 homework

In a college boys and girls are in the ratio of 5 : 8. This year number of boys and girls increased by 20% and 15% respectively. So what is the present ratio of boys and girls in the college?

Thanks

 

[Prove It]

Help me to solve algebra 1 homework

In a college boys and girls are in the ratio of 5 : 8. This year number of boys and girls increased by 20% and 15% respectively. So what is the present ratio of boys and girls in the college?

Thanks

First of all, I want to go to this college ;)

Anyway, when they're in the ratio of 5:8 we can write it as 1:8/5.

If the number of boys is increased by 20%, you end up with another 1/5, giving 6/5:8/5.

If the number of girls is increased by 15%, you end up with another 3/20, giving a ratio of 6/5 : 7/4

Simplifying this ratio we get 6x4 : 7x5, or 24:35.

 

[soroban]

Hello, burgess!

In a college boys and girls are in the ratio of 5 : 8.
This year number of boys and girls increased by 20% and 15% respectively.
What is the present ratio of boys and girls in the college?

We have: $\:\dfrac{B}{G} \,=\,\dfrac{5}{8}$

Multiply by $\frac{1.2}{1.15}\!: \;\dfrac{1.2B}{1.15G} \:=\:\dfrac{1.2}{1.15}\left(\dfrac{5}{8}\right) \:=\:\dfrac{6}{9.2} $

Therefore: $\:\dfrac{1.2B}{1.15G} \:=\:\dfrac{60}{92} \:=\:\dfrac{15}{23}$

 

[burgess]

Thank you all for your responses

 

[CellCoree]

for reaching out for help with your algebra 1 homework. To determine the present ratio of boys and girls in the college, we will need to use the information given to us in the problem. Let's break down the problem into smaller steps to make it easier to solve.

Step 1: Determine the original number of boys and girls in the college.

The original ratio of boys to girls is 5:8, which means for every 5 boys, there are 8 girls. Let's assign a variable to represent the total number of students in the college, x.

This means that there are 5x boys and 8x girls in the college.

Step 2: Calculate the increase in the number of boys and girls.

The number of boys increased by 20%, which can be written as 0.20x. Similarly, the number of girls increased by 15%, which can be written as 0.15x.

Step 3: Add the increase to the original number of boys and girls.

To find the present number of boys, we add the original number of boys (5x) and the increase (0.20x).

So, the present number of boys is 5x + 0.20x = 5.20x.

To find the present number of girls, we add the original number of girls (8x) and the increase (0.15x).

So, the present number of girls is 8x + 0.15x = 8.15x.

Step 4: Simplify the expressions.

We can simplify the expressions by factoring out the common factor of x.

For boys: 5.20x = x(5 + 0.20) = x(5.20)

For girls: 8.15x = x(8 + 0.15) = x(8.15)

Step 5: Determine the present ratio of boys and girls.

Now, we can determine the present ratio of boys and girls by dividing the number of boys by the number of girls.

Present ratio of boys to girls = (x(5.20))/(x(8.15)) = 5.20/8.15

Therefore, the present ratio of boys to girls in the college is approximately 0.64:1 or 64:100.

I hope this helps you with your homework. Keep up the good work in algebra 1!