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Sagot :
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
FINAL ANSWER, AGES TODAY:
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
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
FINAL ANSWER, AGES TODAY:
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
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