Question

Ferdie was having a big party and he was excited. He had been practicing his opening lines all week and as soon as he he got to the part, 20 girls at the party left. There now remained 2 boys for each girl. A lot of the other boys thought the party was pathetic, so 20 of the boys also left. There were now 3 times as many girls as boys. How many boys and girls were at the party when Ferdie got there?

Answer 1

Answer: Boys = 24

Girls = 32

Explanation:

Let the original number of boys = b

Let the original number of girls = g

The following can be further gotten from the question:

When 20 girls left, the equation can be written as:

b = 2(g - 20)

b = 2g - 40 ........ equation i

When 20 boys left, the equation can be written as:

(g-20) = 3(b-20) ......... equation ii

Substitute the value of b into equation ii and solve.

(g-20) = 3(b-20)

g - 20 = 3(2g - 40 - 20)

g - 20 = 3(2g - 60)

g - 20 = 6g - 180

6g - g = 180 - 20

5g = 160

g = 160/5

g = 32

Therefore, the original number of girls = 32.

The original number of boys will be:

b = 2g - 40

b = 2(32) - 40

= 64 - 40

= 24