# Ten years ago, maria's age is 5 times her sons age. if the sum of their ages today is 55 what are their ages now?

1
by hannahmahilum

• Brainly User
2015-09-03T10:55:38+08:00

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Ten years ago:
Son = x
Mother = 5x

Present:
Son:  x + 10
Mother:  5x + 10
Sum of their ages today: 55

Equation:
(x+10) + (5x + 10) = 55
x + 5x + 10 + 10 = 55
6x + 20 = 55
6x = 55 - 20

6x = 35
6       6

x = 35/6

Substitute:
Present Age:
Son:  x + 10
= 35/6 + 10
= 35/6 + 60/6
= 95/6 , or 15 and 5/6 years ,  or 15 years and 10 months

Mother's age:  5x + 10
= 5 (35/6) + 10
= 175/6 + 60/6
= 235/6 , or  39 and 1/6 years,   or  39 years and 2 months

SON'S AGE:  15 and 5/6 years (15 years and 10 months)
MOTHER'S AGE :   39 and 1/6 years (39 years and 2 months)

To check the sum of their ages today:
(x + 10) + (5x + 10) = 55
(35/6  + 10)  +  (5×35/6  + 10) = 55
(35/6 + 60/6) + (175/6 + 60/6) = 55
95/6   +   235/6 = 55
330/6  = 55
330÷6 = 55
55 = 55