Question

Two groups of students, whose average ages are
15 years and 25 years, combine to form a third
group whose average age is 23 years. What is the
ratio of the number of students in the first group
to the number of students in the second group?​

Answer 1

Answer:

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Step-by-step explanation:

Two groups of students, whose average ages are 15 yrs and 25 yrs, combine to form a third group whose average age is 23 yrs. What is the ratio of the number of students in the first group to the number of the second group?

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Two groups of students, whose average ages are 15 yrs and 25 yrs, combine to form a third group whose average age is 23 yrs

Let the number of students in two groups be x and y.

We know average = total sum of ages students / no. of students

Total sum of ages student = average x no.if students

Total sum of ages for group A = 15 × x= 15x

Total sum of ages fir group B = 25×x = 25x

Total sum of ages for both group = 15x + 25x

Total no of students in both group = x + y

Now average age of combined A and B group= total sum of ages if both group / ,total number of students. As such

(15x + 25y) / (x + y) = 23

Cross multiplication

15x + 25y = 23x + 23y

23x + 23y = 15x + 25y

23x - 15x = 25y - 23y

8x = 2y

x / y = 2/8

x / y = 1/4

Ratio between number of students of two groups is 1 : 4