Agroup of 100 students took a quiz their average score was 76 points if the average score of the boys is 80 and the average score of the girls is 70, how many girls participated in the quiz?

40

Step-by-step explanation:

Let the number of boys participating in the quiz be b and the number of girls be g. Since the total number is 100, we have our first equation.

b + g = 100

The average score was 76 points. This means the total score was 76 * 100 = 7600

The average score for the boys was 80 meaning total scores for the boys was 80b while that of the girls was 70g

Hence, we have our second equation:

80b + 70g = 7600

Now let’s put the equations together and solve simultaneously to get g which is the number of girls:

b + g = 100

80b + 70g = 7,600

Let’s simply make a substitution. We can say b = 100 - g. Substituting this will yield:

80(100 - g) + 70g = 7,600

8000 - 80g + 70g = 7600

10g = 400

g = 400/10 = 40

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hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb