Math word problem-10 yrs ago a mother was 3 times as old as her son was. The sum of their ages is 60.?

Question

How old is the mother today? how do you figure that out? what formula do you use? i am trying to explain process to 10 yr old, when i can't even figure it out. please help.

Answer 1

she was 30, he was 10. Now she's 40 and he's 20. 40+20 = 60 I don't know how I figured it out. I just guessed and got it right the first go.

Answer 2

Believe me, I totally understand! These things can blow your mind! (ha)

You want to think this out very slowly.

First let's get some variables. Let x = mom's age, and y = son's age.

Now translate the problem using these variables:

y - 10 = 3(x-10)

See how that is what is written above? y (mom's age now) minus 10 years = 3 times (x (son's age now) minus 10).

So the two equations are:

y - 10 = 3(x - 10)

x + y = 60   (since their ages now add up to 60)

Now rewrite the second equation:

y = 60 - x

And punch this into the first equation in place of y, but first factor out the second equation because it will make it easier:

y - 10 = 3(x - 10)

y - 10 = 3x - 30

(60 - x) - 10 = 3x - 30

60 - x - 10 = 3x - 30

Now solve for x:

-x - 3x = -30 - 60 + 10

-4x = -80

x = 20

So the sons age right now is 20.

Now punch this value into the second equation to get mom's age:

x + y = 60

20 + y = 60

y = 60 - 20

y = 40

So mom's age right now is 40.

And if you subtract 10 from each of these values you will see that ten years ago the son was 10 and the mother was 30, which is three times 10 (the son's age at that time)!

Isn't math fun? :)

Have a good day!

Answer 3

ok so easiest way to do this is break it down

10 years ago mother was 3x her sons age. some of their age now is 60

10 yrs ago and at the age 60 now are both factors of 10...look at all the possibilites

10 and 50

20 and 40

thats it correct?

subtract 10 from each till u can multiply the sons age by 3 and come to the mothers age

0x3 = 0 +40 = 40

10x3=30 + 30 = 60

so the age of the mother was 30

Answer 4

(x -- 10) = 3(60 -- x -- 10) whence 4x = 160 so x = 40, son is 60 -- 40 = 20

mother is 40, son is 20 yrs old.

Answer 5

M = mom's age now

S = son's age now

M - 10 = mom's age 10 years ago

S-10 = son's age 10 years ago

M + S = 60 (sum of their ages is 60)

(M - 10) = 3(S - 10) (mom's age 10 years ago is 3 times her son's age then)

M - 10 = 3S - 30

M = 3S - 20

rearranging the first equation gives M = 60 - S

equate these two:

M = 3S - 20 = 60 - S

4S = 80

S = 20

M = 60 - S = 60 - 20 = 40

So the Mother is 40 now, and the Son is 20 (add to 60)

10 years ago, Mother was 30 and son was 10

(30 = 3(10) check)

this is a system of 2equations you can solve...