Age Problem 8 Solution

This is the solution to the algebra  age problem asked by Joshua that read, "A man is 4 years older than his wife and 5 times as old as his son. When the son was born, the age of the wife was six-sevenths that of her husband's age. Find the age of each."
Ok so here we go...

"A man is 4 years older than his wife"
m = w + 4
Now we will subtract 4 from both sides to use this conveniently later ( you will see)
w = (m-4)

"and 5 times as old as his son."
m = 5s

"When the son was born, the age of the wife was six-sevenths that of her husband's age."
w - s = 6/7(m-s)

7(w-s) = 6(m-s) -->
7w - 7s = 6m - 6s --->
7w = 6m - 6s + 7s --->
7w = 6m + s
replace w with (m-4)
7(m-4) = 6m + s
7m - 28 = 6m + s
7m - 6m = s + 28
m = s + 28
replace m with 5s
5s = s + 28
5s - s = 28
4s = 28
s = 7 yrs is the son's age
then
5(7) = 35 yrs is Dad's age
and
35-4 = 31 yrs is Mom's age

Now check work...
"When the son was born, the age of the wife was six-sevenths that of her husband's age."
31 - 7 = 6/7(35 - 7)
24 = 6/7*28
24 = 24;

Age Problem 7 Solution

This is the solution to a algebra age word problem as asked by a anonymous user: "Nona is one-third as old as her mother. Five years ago, she was only one-fifth of the age of her mother. How old is Nona now? "


It is easier to set this up with two unknowns say x and y and have 2 equations.

The 1st equation would be:  x = 1/3(y)  or x = y/3   since Nona is currently 1/3 as old as her mother.  Now 5 years ago she was only 1/5th the mothers age so the other equation would be..

x -5 = 1/5(y - 5)   multiply by 5..

5x - 25 = y - 5 so

y = 5x - 20  .. plug this back into the 1st equation and you get..

x = (5x - 20)/3  - -multiply by 3

3x = 5x - 20  so 2x = 20  and x = 10

So Nona is 10 years old currently and the mom is 30.   To check this go 5 years back... Nona would be 5 and the mother would be 25   ------   5/25 = 1/5ths of her mothers age...

Age Problem 6 Solution

This is the answer to the age algebra word problem that asked, "Bob is one third the age of his father. In 12 years he will be half the age of his father. How old is each now?"


Ok Bob being 1/3 the age of his father is the same thing as saying the father is 3 times as old as him.  It makes it easier to work with.  So let Bob be x and his father be 3x. And in 12 years bob will be half as old as his father.  So we have..


x + 12 =  (3x + 12) / 2

2x + 24 = 3x + 12

x  = 12


So Bob is 12 years old and his father is 3(12) or 36 years old now.  In 12 years Bob will be 12 + 12  or 24 years old and his father will be 36 + 12 or 48 years old which means Bob will be half as old so it checks out.

Age Problem 5 Solution

This is the algebra age word problem that read Pol is 10 years younger than greg. In 7 years, he will be 10 years more than one halfas old as greg. Find their age at present. help me solve it.

Let Greg be X and Pol be X - 10 as far as current ages.  In 7 years (thats x + 7) he will be 10 years more than 1/2 as old as greg (thats (x - 10 + 10)/2 or x/2).  So set them equal..

X  and x -10

x + 7  and  x - 10 + 7  28  and 25 



(x+7)/2 + 10 = x - 3

x + 17 = 2x - 6  ******** Correction    2 * 10 = 20 + 7 = 27 So it should be

x + 27 = 2x - 6

x =33  ---> Which is Greg's age so Pol's is x-10 or 33 -10 = 23 

So Pol is 23 and Greg is 33

Age Problem 4 Solution

This is the solution to the algebra age problem # 4... "A man is 27 years older than his son and 10 years from now, he will be twice as old as his son. how old is each now?"

Let x = the son and x + 27 = the man(father)

in 10 years the son will be x + 10 and the father x + 27 + 10 or x + 37 years old. So if he will be twice as old as his son then "twice" the sons age then will "equal" each other.

So, 2(x+10) = x + 37
multiply by 2 on the left side

2x + 20 = x + 37

x = 17 This makes sense since 10 + 17 = 27 and 17 + 37 = 54 which is twice the sons age 10 years from now. So the son is 17 and the father is 17 + 27 or 44 years old.

Tags: Age Problem Solutions, Algebra Word Problem Solutions

Age Problem 3 Solution

Greg will be x and Greg's father will be x + 30. In 15 years Greg will be x + 15 and Greg's father will be x + 30 + 15 or x + 45, and the sum of their ages will be 130.

So,

x + 15 + x + 45 = 130

2x + 60 = 130

2x = 130 - 60

2x = 70

x = 70/2

x = 35 which is Greg's current age. Greg's father is 35 + 30 or 65 years old. Just to check add 15 years or 30 total to their ages. 35 + 65 + 30 = 130

Age Problem 2 Solution

Here's a non-algebraic approach to the problem:

If Bobs current age were 8 then 8 years ago he would be zero, so he has to be older than 8 or at least 9 years now. So assume 9 and 36 -- 8 years ago would make 1 and 28 which is 28 times and not what were looking for.. 10 and 40 ---- 8 years ago would make 2 and 32 which is 16 times not what were looking for... try 11 and 44-- 8 years ago would make 3 and 36-- bingo 12 times- So, Jason is 44 and Bob is 11 years old.

Algebraically we have:

x for Bobs age and

4x for Jason

So 4x = x

But 8 years ago Jason was 12 times older so

4x - 8 = 12(x-8)

4x - 8 = 12x - 96

88 = 8x

x = 11 So Bob is currently 11 years old and Jason is 4(11) or 44 years old.

Age Problem 1 Solution

For a non-algebraic approach:

If Steves current age was 20 then 20 years ago he would be zero, so he has to be at least 21 years old. This would make Bob 42 and Steve 21. 20 years ago they would be 22 and 1, which is 22 times as old and not 6 times. Were not that far off though. So go up by increments. Try Steve at 22 and Bob 44-- 20 years ago would be 2 and 24 which is 12 times-- at 23 and 46 we can see than 20 years ago they would be 3 and 26 which is over 8 times were close-- and at 24 and 48 20 years ago would make 4 and 28 which is 7 times and really close.. at 25 and 50 20 years ago we would have 5 and 30 which IS 6 times older and what were looking for. So, Steve is 25 and Bob is 50...


For the algebraic approach we know that if something is twice as old, big, fast, etc as something else it is 2x more than x. So in this problem Bob is 2x as old as x Steve is.

Twenty years ago would be :

2x - 20 for Bob

and

x - 20 for Steve

but, 20 years ago Bob was 6 times older so

2x - 20 = 6(x - 20)

2x - 20 = 6x - 120

4x = 100

x = 100/4

x = 25

So x or Steve is 25 and Bob is twice or 2(25): 50 years old.