There are 12 boys and 10 girls in your gym class. If 6 boys joined the class, how many girls would need to join for the ratio of boys to girls to remain the same?
find the common ratio e.g if they gave 20:10 the ration would be 10:5
turn the ratios into fractions
12 over 10 & 18 over x
cross multiply
10 x 18 = 180
divide 180 by 12.
180 / 12 = 15
check to make sure they are equivalent
15 - 10 = 5
answer: 5 girls would need to join the class.
To find out how many girls would need to join the class, we need to determine the ratio of boys to girls before and after the boys joined the class.
Before the boys joined, the ratio of boys to girls was 12:10, which simplifies to 6:5.
After 6 boys join, the new total number of boys is 12 + 6 = 18.
To maintain the same ratio, we want the ratio of boys to girls to still be 6:5.
So, we need to find the number of girls, x, that satisfies the equation:
18 / (10 + x) = 6 / 5
To solve for x, we can cross-multiply:
18 * 5 = 6 * (10 + x)
90 = 60 + 6x
Subtracting 60 from both sides:
90 - 60 = 6x
30 = 6x
Dividing both sides by 6:
30 / 6 = x
x = 5
Therefore, 5 girls would need to join the class for the ratio of boys to girls to remain the same.
What do you think?
I'll give you a hint: whenever you add something to one side, in order to keep the difference equal youuuuuu-?