Question

you see my avatar...this is what my real face looks like when I am viewing this problem...except I am not yellow

Answer 1

My grandson is as many days as my son is in weeks. My grandson is as many months as I am in years. We are all three, when added together, 120 years. How old am I , in years ?

Answer 2

m + g + s = 120

thats all I got

Answer 3

I have no idea

Answer 4

why ?

Answer 5

I have one equation.....I don't know where to go from there

Answer 6

Let g = age of granson in days
Let s = age of son in weeks
Let m = my age in years

Let's convert all ages to days.

m + g + s = 120(265.25)

Answer 7

wait...where did you get the 265.25 ?

Answer 8

There are 365.25 days in a year.

Answer 9

oh....but you got 265.25...why are you subtracting 100

Answer 10

typo

Answer 11

ok...I got you

Answer 12

The problem is you need to make an assumption of how many days per month.

Answer 13

30 on average

Answer 14

Let's do it your way with everything in years.
Your first equation is good.

Answer 15

m + g + s = 120
Keep in mind that m, s, and g are all in years.

Answer 16

ok

Answer 17

"My grandson is as many days as my son is in weeks."
We need to change the above statement into an equation.

Answer 18

How many days are there in g years?
How many weeks are there in s years?

Answer 19

365.25 days
52 weeks/year

Answer 20

365.25g = 52s ??

Answer 21

Ok, so g years = 365.25g days
s years = 52s weeks
365.25g = 52s
You are correct.

Answer 22

Now we have tw equations.
We need one more.

Answer 23

do I solve for g ?

Answer 24

Not yet.
Let's get our 3rd equation so we end up with a system of three equations in three unknowns.

"My grandson is as many months as I am in years."

Answer 25

12g = m ??

Answer 26

g years = 12g months
m years = m years
12g = m
Great. You got it.

Answer 27

m + g + s = 120
365.25g = 52s
12g = m

Answer 28

ok...
m + g + s = 120
365.25g = 52s
12g = m

so I sub 12g in for m in the 1st equation ?

Answer 29

Yes

Answer 30

12g + g + s = 120
13g + s = 120
13g = 120/s

Answer 31

and then the first 2 eqs are a system of 2 eqs in 2 unknowns.

Answer 32

Careful:
13g + s = 120
13g = 120 - s

Answer 33

Now solve for g:
13g = 120 - s

Answer 34

13g = 120 - s
g = (120 - s)/13
g = 9.23 - s/13

Answer 35

Now use the second equation:
365.25g = 52s
Substitute g with 9.23077 - s/13

Answer 36

365.25 (9.23077 - (s/13) = 52s

Answer 37

365.25(9.23077 - s/13) = 52s

Answer 38

Good.
Multiply out the left side.

Answer 39

3371.538 - 28.096s = 52s

Answer 40

3371.5387425 - 365.25s/13 = 52s
do I multiply the equation by 13 ?

Answer 41

oops

Answer 42

Don't erase. You're ok.

Answer 43

3371. 538 = 52s + 28.096s
am I on the right track

Answer 44

great

Answer 45

Add the right side.
Divide both sides by the number multiplying s.

Answer 46

3371.538 = 80.096s
3371.538/80.096 = s
42.0937 = s

Answer 47

Great. You got one of them.

Answer 48

Now use s here to get g.
365.25g = 52s

Answer 49

13g = 120 - s
13g = 120 - 42.0937
13g = 77.9603
g = 77.9603/13
g = 5.9928

Answer 50

oops...I did the wrong one

Answer 51

Excellent.
Finally, use 12g = m to find m.

Answer 52

It makes no difference which eq you use as long as it's a correct eq.

Answer 53

12(5.9928) = m
71.9136 = m

Answer 54

do I round any numbers.....would m be 72

Answer 55

Ok, so in years the ages are:
Grandparent (me) m = 71.9
Son s = 42.1
Grandson g = 5.99
Right?

Answer 56

m + g + s = 120
71.9 + 5.99 + 42.1 = 120
119.99 = 120
rounded
120 = 120
yes....
wow, I am 72...I feel that old

Answer 57

thank you soooooooo much

Answer 58

Let's see if our answers make sense with the given info.
"My grandson is as many days as my son is in weeks."
5.99(365.25) = 2188 days old for grandson
42.1(52) = 2189 weeks old for son
This checks out.

Answer 59

your the best

Answer 60

"My grandson is as many months as I am in years."
5.99(12) = 72 months for grandson
72 grandparent's age in years
This also checks out.

Answer 61

you should be a teacher

Answer 62

Finally, he one you already checked:
"We are all three, when added together, 120 years."
71.9 + 5.99 + 42.1 = 120
This checks out, too.

Answer 63

You did a great job.
Thanks for you nice comment.

Answer 64

you did a better job.....thanks again

Answer 65

You can now fix your avatar to a nice smile!
You're welcome.

Answer 66

lol...I might just do that