The ratio of the number of girls to the number of boys in a stamp club was 3 : 2 last year. When 15 boys joined the club this year, the ratio became 2 : 3. Find the total number of children in the club this year.
let the number of girls be 3x and the number of boys 2x
(notice 3x : 2x = 3 : 2 )
after the addition of boys
number of girls = 3x
number of boys = 2x + 15
3x : 2x+15 = 2:3
3x/(2x+15) = 2/3
9x = 4x + 30
5x = 30
x = 6
current number of girls = 18
current number of boys = 27
so number of children in the club now
= 3x + 2x+15 = 5x + 15
= 5(6) + 15 = 45
check:
original: girls = 18, boys = 12, notice ratio is 18:12 = 3:2
after: girls = 18 , boys = 27 , notice 18:27 = 2:3
and 18+27 = 45
all is well.
Well, it seems like those boys brought quite a "stampede" into the club this year! Let's use our math skills to figure this out.
So, last year the ratio of girls to boys was 3:2. Let's say there were 3x girls and 2x boys in the club last year.
Now, this year, when 15 boys joined, the ratio became 2:3. That means we have 2 girls for every 3 boys. We can set up the equation 2/3 = (3x)/(2x + 15) and solve it.
Cross-multiplying, we get 2(2x + 15) = 3(3x).
Simplifying further, we have 4x + 30 = 9x.
Subtracting 4x from both sides of the equation, we get 30 = 5x.
Dividing both sides by 5, we find x = 6.
So, there were 3(6) = 18 girls last year and 2(6) = 12 boys.
This year, 15 boys joined, making the total number of boys 12 + 15 = 27.
Therefore, the total number of children in the club this year is 18 (girls) + 27 (boys) = 45.
So, the total number of children in the club this year is 45. Don't forget to "stamp" your answer!
Let's assume that last year, the number of girls in the stamp club was 3x, and the number of boys was 2x.
After 15 boys joined this year, the number of girls remained the same because the question only mentions that boys joined. So, the number of girls this year is still 3x.
Now, the number of boys this year is 2x + 15.
According to the given information, the ratio of girls to boys this year is 2:3. So we can set up the following equation:
3x / (2x + 15) = 2 / 3
Cross-multiplying, we get:
9x = 4x + 30
Subtracting 4x from both sides, we get:
5x = 30
Dividing both sides by 5, we get:
x = 6
So the number of boys this year is: 2x + 15 = 2(6) + 15 = 12 + 15 = 27.
And the number of girls this year is: 3x = 3(6) = 18.
To find the total number of children in the club this year, we add the number of boys and girls:
27 + 18 = 45.
Therefore, the total number of children in the club this year is 45.
To find the total number of children in the club this year, we need to use a system of equations.
Let's assume that the initial number of girls in the club last year is 3x and the initial number of boys is 2x.
According to the information given, the ratio of girls to boys last year was 3:2. So we have the equation: (3x)/(2x) = 3/2.
Simplifying the equation, we get: 3x * 2/2x = 3/2, which gives us: 6x/2x = 3/2.
Simplifying further, we get: 3 = 3/2.
This tells us that the ratio was the same this year as it was last year. This means that the number of girls and boys increased by the same factor.
Now, let's look at the information given about this year. The ratio of girls to boys is 2:3. So we have the equation: (3x + 15)/(2x) = 2/3.
Simplifying this equation, we get: (3x + 15) * 3/2x = 2/3.
Now, we can solve for x:
(3x + 15) * 3 = 2 * 2x.
Expanding the equation, we have: 9x + 45 = 4x.
Subtracting 4x from both sides, we get: 5x + 45 = 0.
Subtracting 45 from both sides, we get: 5x = -45.
Dividing both sides by 5, we get: x = -9.
It doesn't make sense to have a negative number of children in the club, so the value of x must be positive.
Therefore, there is no solution to this problem given the current information. Please check the problem statement or provide additional information.