Question

The sum of a man's age and his grandmother's age is 102. Eighteen years ago his grandmother was 10 times as old as he was then. What are their present ages?

Answer 1

Let the man's present age be x and grandmother's present age be y.
x+y=102
y-18=10(x-18)
y-18=10x-180
y=10x-162
x+10x-162=102
Can u solve for x?

Answer 2

So 10x is negative?

Answer 3

no.

Answer 4

See if u can solve nw.
11x-162=102

Answer 5

x is age. so 10x can not be negative. do u get it?

Answer 6

why do you add it to x?

Answer 7

It is given that the sum of present ages of the man and his grandmother is 102.
I assumed man's present age to be x nd grandmother's present age to be y.
So x+y=102.
Is that clear?

Answer 8

yes

Answer 9

Nw can u tell me the age of the man 18 yrs ago in terms of x and number?

Answer 10

x-18?

Answer 11

yup. vat about grandmother's age 18 yrs ago?

Answer 12

60?

Answer 13

no. I meant in terms of y and number.

Answer 14

oh, y-18

Answer 15

u r right.
It is given that the age of grandmother 18 yrs ago was 10 times the age of the man's age 18 yrs ago.
So
y-18=10(x-18)
Is that clear?

Answer 16

yes.
So y-18=10x-180

Answer 17

ya.

Answer 18

So y=10x-162

Answer 19

ya

Answer 20

Nw subtitute that in
x+y=102
and solve for x to find the man's present age. Can u?

Answer 21

x+10x-162=102
11x-162=102
11x=264
x=24

Answer 22

ya perfect.
Nw can u find y?

Answer 23

24-18=6(man's age 18 years ago)
6x10=60(Grandmother's age 18 years ago)
60+18=78(grandmother's present age)

Answer 24

perfect.:)

Answer 25

oh my god. thank you so much for your help!! :)

Answer 26

yw.:)