How many 👧 are in the class? 🏫

[ParanoidUser]

In the class, 1/3 of the students brought a teddy 🐻.
Each 👦 took 12 📗, each 👧 took 17 📕, and each teddy 🐻 took 9 📘.
A total of 305 📚 were taken out.

[peterbaccaro]

There are 7 girls in the class.

Reasoning

number of boys = b
number of girls = g

1/3 of the students brought a teddy so number of teddy bears is b + g / 3

number of books boys took = 12b
number of books girls took = 17g
number of books teddy bears took = 9 * (b + g / 3)
number of books teddy bears took simplified = 3(b + g)

So 12b + 17g + 3(b + g) = 305
Simplified as 12b + 17g + 3b + 3g = 305
Simplified as 15b + 20g = 305
Simplified as 3b + 4g =61

So g = (61 - 3b) / 4

number of boys (b) and girls (g) needs to be a whole number greater than 0 so you can put values for b and see if g is a whole number.

The values of b where g is a whole number are:

• If b is 3 then g = 52/4 = 13
• If b is 7 then g = 49/4 = 10
• If b is 11 then g = 46/4 = 7
• If b is 15 then g = 43/4 = 4
• If b is 19 then g = 40/4 = 10

number of bears also needs to be a whole number greater than 0.

• If b is 3 and g = 13 then teddy bears would be = 16/3 = 5.33
• If b is 7 and g = 10 then teddy bears would be = 17/3 = 5.66
• If b is 11 and g = 7 then teddy bears would be = 18/3 = 6
• If b is 15 and g = 4 then teddy bears would be = 19/3 = 6.33
• If b is 19 and g = 10 then teddy bears would be = 20/3 = 6.66

Since only one of the above options results in a whole number of teddy bears we have the answer.

So there are 11 boys, 7 girls and 6 teddy bears in the class.