### A sister is 10 years older than her brother, the sum of their ages is...

A sister is 10 years older than her brother, the sum of their ages is 32yrs,find their ages.?

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Good afternoon.

Let the age of the sister= S;
the age of the brother= B.

So, the relationships are:

S= B + 10 •••> (1)
S + B= 32 •••> (2)

Therefore, we input the value of S in equation (1) in equation (2) first,

S + B= 32
B + 10 + B= 32
2B + 10= 32
2B= 32 - 10
2B= 22
B= 22/2
B= 11

then we substitute the value of B above in equation (1).

S= B + 10
S= 11 + 10
S= 21

Thus, the ages of the sister and the brother are 21 and 11 respectively.

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Let brother age be Y and Sisters age be X
X+Y=32....... 1
And X=Y+10.....2.... sub eqn 2 in 1
Y+10+Y=32
2Y=32-10
2Y=22
Y=22/2=11
Y(Brother is) 11years

sisterX(Y+10) 11+10=21years
X+Y=32years
21+11=32years
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Their ages are 11 and
21
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