SOLUTION: Sophia mother’s age is thrice more than her daughter. If the sum of theirs ages is 40, what is the ratio of the age of Sophia’s mother to that of Sophia?

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Question 175017: Sophia mother’s age is thrice more than her daughter. If the sum of theirs ages is 40, what is the ratio of the age of Sophia’s mother to that of Sophia?
Found 2 solutions by Mathtut, actuary:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
let sophia and mom's age be s and m(dont read anything into the s&m thing..lol)
:
m=3s......eq 1
s+m=40....eq 2
:
place m's value of 3s from eq 1 into eq 2
:
s+3s=40
:
4s=40
:
highlight%28s=10%29sophia's age
:
highlight%28m=3s=3%2810%29=30%29mom's age

Answer by actuary(112) About Me  (Show Source):
You can put this solution on YOUR website!
Let Sophia age be x and Sophia's mother's age be y.
x+y = 40 (Equation #1)
and y=3*x (Equation #2)
Substitute the formula for "y" into equation #1
x+3*x=40
Add the terms with an "x"
4*x = 40
Solve for x
x = 10
From Equation #2 y = 3*x = 3*10=30
The ratio of the age of Sophia’s mother to that of Sophia is y/x = 30/10=3
Actually, the answer could have been obtained directly from equation #2
y=3*x so y/x=3