Question

In a class the average weight of 150 students is 80 kg. the average weight of boys and girls is 85 kg and 70 kg respectively. the number of girls in the class is

Answer 1

Define x:

Let the number of boys be x

The number of girls = 150 - x

Find the weight of all the 150 students:

Average weight of the 150 students = 80 kg

Total weight of the 150 students = 80 x 150 = 12000 kg

Find the total weight of the boys:

Average weight of the boys = 85 kg

Total weight of the boys = 85x

Find the total weight of the girls:

Average weight of the girls = 70 kg

Total weight of the girls = 70 (150 - x) = 10500 - 70x

Form the equation and solve for x:

85x + 10500 - 70x = 12000

15x = 1500

x =  100

Find the number of girls

Number of girls = 150 - x = 150 - 100 = 50

Answer: There are 50 girls

Answer 2

here is your answer OK

Let the number of boys be B and the number of girls, G. Let us form the equation from the given statements.

B + G = 150 … (1).

The total weight of boys and girls is

70B + 55G = 150*60 = 9000 … (2)

The HCF in (2) is 5, so dividing right through by 5 we get

14B + 11G = 1800 … (3)

Multiply (1) by 11 to get

11B + 11G = 150*11 = 1650 … (4).

Subtract (4) from (3) to get

14B + 11G -11B - 11G= 1800 - 1650, or

3B = 150. or B = 50, then G = 150 - 50 = 100.

Check: Total weight of B and G = 50*70 + 100*55 = 3500+5500 = 9000.

Answer: Boys = 50, Girls = 100.