Question

the difference in ages between a boy and his younger brother is 6 years older than his sister.the sum of ages of the younger brother and his sister is 30.How old are the three children?​

Answer 1

Explanation:

let b = the boy's age

let y = the younger brother's age

let s = the sister's age

:

write an equation for each statement, arrange to have b and s in terms of y

;

The difference in ages between a boy and his younger brother is 6 years.

b - y = 6

b = y + 6

the younger brother is 6 years older than his sister.

y = s + 6

s = y - 6

the sum of ages if the younger brother and his sister is 30.

b + y + s = 30

replace b with (y+6), replace s with (y-6)

(y+6) + y + (y-6) = 30

combine like terms

3y = 30

y = 30/3

y = 10 yrs is younger bro's age

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how old are the three children?

b = 10 + 6 = 16 yrs is the boy's age

and

s = 10 - 6 = 4 yrs is the sister's age

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