SOLUTION: PROBLEM A woman is 5 years older than her husband and 10 times as old as their daughter. In 14 years, the sum of their ages will be 100. How old is each one now? ___________ __

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Question 82784: PROBLEM
A woman is 5 years older than her husband and 10 times as old as their daughter. In 14 years, the sum of their ages will be 100. How old is each one now?
________________________________________________________________________________

Woman= h+5
Husband= h
Daughter=h+5/10(I think)
+________
100
(h+5)+(h)+(h+5/10)=100
2h+5+(h+5/10)=100
3h+10=1000
3h/3=990/3
h=330
My question is what did i do wrong I know that this is way too high of a number and I can't figure out where I went wrong. Thanks
Found 4 solutions by jim_thompson5910, rapaljer, stanbon, scott8148:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let w=woman, h=husband, d=daughter
Set up the following equations:
w=h%2B5 "A woman is 5 years older than her husband". Notice if h=30, w=40 which is 10 years older.Solving for h we get
h=w-5

w=10d "the woman is 10 times as old as their daughter". Notice if d=2, then w=20 which means the woman is 10 times older. Solving for d we get
d=w%2F10

So in 14 years the woman's age is

w=w%2B14

In 14 years the husband's age is

h=h%2B14

and in 14 years the daughter's age is

d=d%2B14

Adding these together we get

%28w%2B14%29%2B%28h%2B14%29%2B%28d%2B14%29=100

%28w%2B14%29%2B%28%28w-5%29%2B14%29%2B%28%28w%2F10%29%2B14%29=100Plug in h=w-5 and d=w%2F10 (we solved for these earlier). This eliminates every variable but w, which means we can solve for w now.

2w%2B37%2Bw%2F10=100 Combine like terms

10%282w%2B37%2Bw%2F10%29=10%28100%29Multiply both sides by 10. This will eliminate the denominator.

20w%2B370%2Bw=1000%29 Distribute

21w%2B370%2Bw=1000%29 Combine like terms

21w=630 Subtract 370 from both sides

w=30 Divide both sides by 21

So the woman is 30 years old. In 14 years she will be 44 years old. The husband's age is:

h=w-5
h=30-5=25 plug in w=30

So the husband is 25 now and in 14 years he will be 39. Finally the daughter's age is:

d=w%2F10

d=30%2F10=3 plug in w=30

So the daughter is 3 years old now and in 14 years will be 17 years old. So if we add everyone's future age (ie their age in 14 years) together we get:
future_age_woman%2Bfuture_age_husband%2Bfuture_age_daughter=100
44%2B17%2B39=100
100=100 works
This verifies our answer.


note: you forgot to factor in the 14 year time lapse. That would explain the large age answer you got. Also, I'm not sure how you got Daughter=h+5/10

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct in your set up of the problem:
Woman= h+5
Husband= h
Daughter=(h+5)/10

However, the equation has to do with the sum of their ages in 14 years. These are the ages in 14 years:

Woman= h+5 +14
Husband= h +14
Daughter=(h+5)/10 + 14

The equation should be:
(h+5)+14 +(h)+14 +((h+5)/10)+14 =100

Subtract 14*3 = 42 from each side, and your equation will equal 58 instead of 100. Try that and see if it works. I think you may have had another error as well:
(h+5) +(h) +((h+5)/10) =58
2h+5 + (h+5)/10 = 58
20h + 50 + h+5 = 580
21h + 55 = 580
21h = 525
h= 525/21 = 25 years old = Husband
w = 30 years old = Wife
d = 30/10= 3 years old = Daughter

In 14 years:
Husband will be 39
Wife will be 44
Daughter will be 17

Check: 39+44+17= 100 years young!!

R^2 at SCC

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A woman is 5 years older than her husband and 10 times as old as their daughter. In 14 years, the sum of their ages will be 100. How old is each one now?
-----------
NOW DATA:
Let the daughter's age be "x".
Mother age is 10x
Husbands age is 10x-5
---------------------
14 Years from now DATA:
Daughter's age will be x+14
Mothers age will be 10x+14
Husbands age will be 10x-5+14 = 10x+9
-------------------
EQUATIOn:
x+14 + 10x+14 + 10x+9 = 100
21x+37=100
21x = 63
x=3 (daughter's age NOW)
10x = 30 (mother's age NOW)
10x-5 = 25 (husband's age NOW)
==============
Cheers,
Stan H.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you have the age relationships right, but everyone will be 14 years older when their ages sum to 100

when you multiplied 2h+5+((h+5)/10)=100 by 10 you should have gotten 20h+50+h+5=1000 or 21h+55=1000

if you use the daughter's age as a base, then you avoid the fractions that led to your calculation error

(d+14)+(10d+14)+(10d-5+14)=100 ... 21d+37=100 ... d=3 so w=30 and h=25