Question

8. The ratio of the number of boys to the number of girls in a dance club is 5 : 6.

After 6 more boys join the club, the ratio became 13:12.
a) How many members of the club are girls?
b) How many boys are members of the club in the end?

Answer 1

To find the number of girls and boys in the club, we can set up a proportion using the given ratios. By solving the proportion, we can find that there are 24 girls and 26 boys in the club after 6 more boys join.

Step-by-step explanation:

To solve this problem, we can set up a proportion. Let's say the number of boys in the club is 5x and the number of girls is 6x. After 6 more boys join, the ratio becomes 13:12, so the new ratio is (5x+6):(6x). We can set up the proportion: (5x+6)/(6x) = 13/12.

Next, we can cross-multiply to get: 12(5x+6) = 13(6x).

Simplifying this equation gives us: 60x + 72 = 78x.

Bringing like terms together, we have 18x = 72.

Dividing both sides by 18 gives us x = 4.

Now we can find the number of girls by substituting x back into the original ratio: 6x = 6(4) = 24 girls.

Lastly, to find the number of boys in the club after 6 more join, we add 6 to the original number of boys: 5x + 6 = 5(4) + 6 = 26 boys.

Answer 2

a, 18 girls

b. 21 boys

Step-by-step explanation:

a) To find the number of girls in the club, we can use the fact that the ratio of boys to girls is 5:6. If we let x be the number of girls in the club, then the number of boys is 5/6x.

When 6 more boys join the club, the new ratio is 13:12.

We can set up the equation: (5/6x)+6 = (13/12*x).

Solving for x gives us x = 18.

So there are 18 girls in the dance club.

b) To find the number of boys in the club in the end, we can use the new ratio of 13:12 and the number of girls we found earlier (18). If we let y be the number of boys in the club in the end, then the number of girls is 12/13y.

We can set up the equation: 18 = (12/13y)

Solving for y gives us y = 21.

So there are 21 boys in the dance club in the end.