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Preliminary algebra problem really!

Let Fred and Mary be denoted by F and M respectively

Mary being x years old.

Therefore, M=x and F=x+3

In 7 years time, M=x+7 and F=x+3+7

Now, given that M is 6/7th years as old as F seven years later,

M=(6/7)(F), which becomes M=(6/7)(x+10) {EQUATION 1}

Equating EQUATION 1 with M=x+7 and solving for x gives x=11

Therefore Mary is 11 years old while Fred is 11+3, 15 years old (Seven years ago).

Posted on Jun 03, 2012

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Fred is 14 and Mary is 11

Posted on Jun 08, 2011

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Hi.

Algebra !!!!! can't stand it.

Anyway here is the answer >>>>>

Mary is 11 and Fred is 14

Regards.

Posted on Jun 08, 2011

Fred = Mary +3

7*mary = 6/7 *Fred

substitute fred =mary + 3

7m = 6/7 * (mary + 3)
7m = 6/7*m + 6/7*3
7m - 6/7*m = 6/7*3
m(7-6/7)= 6/7*3

m = (6/7*3) / (7-6/7)
m=0.419 years old

substitue m into fred = mary+3
Fred = 3.419 Years old

Posted on Jun 08, 2011

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Posted on Jan 02, 2017

Let Adjoa's age be x and Kwame's y.

- Adjoa is 3 years older than Kwame: x=y+3
- Seven years ago sum of their ages was 13: (x-7)+(y-7)=13
- Now you substitute first equation into second equation: (y+3-7)+(y-7)=13
- 2y-4-7=13
- 2y=24
- y=24/2=12 years
- x=y+3=12+3=15 years
- sum of their present ages is x+y=12+15=27 years

Sep 27, 2011 | Office Equipment & Supplies

Let x be Diophantus' age when he died.

His son died 4 years before Diophantus (so Diophantus was then x-4 years old). His son lived half as long as Diophantus so when he (son) died he was x/2.

Diophantus' son was born when Diophantus was (x-4)-x/2 years old. That was 5 years after his marriage so when Diophantus married he was (x-4)-x/2-5 years old. We also know that 1/6 of his life was spent in childhood, 1/12 in youth and 1/7 as bachelor so (x-4)-x/2-5=(1/6+1/12+1/7)x.

Now you solve last equation:

Diophantus was 84 years old when he died.

His son died 4 years before Diophantus (so Diophantus was then x-4 years old). His son lived half as long as Diophantus so when he (son) died he was x/2.

Diophantus' son was born when Diophantus was (x-4)-x/2 years old. That was 5 years after his marriage so when Diophantus married he was (x-4)-x/2-5 years old. We also know that 1/6 of his life was spent in childhood, 1/12 in youth and 1/7 as bachelor so (x-4)-x/2-5=(1/6+1/12+1/7)x.

Now you solve last equation:

- x-4-x/2-5=11/28x
- x/2-11/28x=4+5
- 3/28x=9
- x=9*28/3=84 years

Diophantus was 84 years old when he died.

Sep 27, 2011 | Office Equipment & Supplies

Todd is 4 years old.

Let Tom's age = X

Let Todd's age = Y

From the given facts:

X = 5Y

and

X + 7 + 6 = 3 ( Y + 7 )

X+13 = 3Y + 21

X = 3Y + 8

So if:

X=5Y

and

X=3Y+8

Then:

5Y=3Y+8

2Y=8

Y=4

I hope that helps.

Joe.

Let Tom's age = X

Let Todd's age = Y

From the given facts:

X = 5Y

and

X + 7 + 6 = 3 ( Y + 7 )

X+13 = 3Y + 21

X = 3Y + 8

So if:

X=5Y

and

X=3Y+8

Then:

5Y=3Y+8

2Y=8

Y=4

I hope that helps.

Joe.

Sep 14, 2011 | Office Equipment & Supplies

let c = cory's age now
let s = her sisters age now

cory's age now = sisters age + 6 years

=> c = s + 6

4 years ago, cory was 4 years younger ( i.e. c-4) and her sister was 4 years younger (s- 4)

4 years ago cory was 4 times older than her sister

=> c - 4 = 4*(s-4)

We can simplify this to c = 4s - 16 +4 c = 4s - 12

We can then use simultaneous equations to solve the two equations

(i) c = s + 6 (ii) c = 4s - 12

If we multiply both sides of equation (i) by 4 we get (iii) 4c = 4s + 24

We can then subtract equation (ii) from equation (iii) to eliminate the '4s' term => ( 4c = 4s + 24 ) - (c = 4s - 12) => 4c - c = 4s +24 - 4s +12 => 3c = 4s - 4s +36 => 3c = 36 => c = 36/3 => c = 12 => Cory's age now = 12

__For clarity:__
Her sister's age now is of course 6
4 years ago Cory would of been 8 and her sister would of been 2

I hope this helps and good luck! If you have more questions - ask away!

Please take the time to rate this answer

Many Thanks Don.

cory's age now = sisters age + 6 years

=> c = s + 6

4 years ago, cory was 4 years younger ( i.e. c-4) and her sister was 4 years younger (s- 4)

4 years ago cory was 4 times older than her sister

=> c - 4 = 4*(s-4)

We can simplify this to c = 4s - 16 +4 c = 4s - 12

We can then use simultaneous equations to solve the two equations

(i) c = s + 6 (ii) c = 4s - 12

If we multiply both sides of equation (i) by 4 we get (iii) 4c = 4s + 24

We can then subtract equation (ii) from equation (iii) to eliminate the '4s' term => ( 4c = 4s + 24 ) - (c = 4s - 12) => 4c - c = 4s +24 - 4s +12 => 3c = 4s - 4s +36 => 3c = 36 => c = 36/3 => c = 12 => Cory's age now = 12

I hope this helps and good luck! If you have more questions - ask away!

Please take the time to rate this answer

Many Thanks Don.

Sep 13, 2011 | Sunburst My Mathematical Life Single...

Let the brother's age be x:

16years for Mary = 4x years for Brother

From equation: 4x = 16

x = 4

Therefore, the brother is 4 years old.

__Mary__ __ Brother__

16 4

After 4 years +__4 4__

20 8

After the next 4 years +__4 4__

24 12

24 is twice as old as 12; therefore for the sister to be twice as old as brother she will 24years when her brother is 12 years.

Or by calculation;

If 4 is the age for the brother, when the sister is 16, and y years will pass for the to be such that the sister is twice as old as the brother, then;

16 + y = 2(4 + y)

16 + y = 8 + 2y

16 - 8 = 2y - y

8 = y

Therefore, 8 years elapse before the sister is twice as old as the brother.

Sister will be: (16 + 8) = 24years

Brother will be: (4 + 8) = 12years

16years for Mary = 4x years for Brother

From equation: 4x = 16

x = 4

Therefore, the brother is 4 years old.

16 4

After 4 years +

20 8

After the next 4 years +

24 12

24 is twice as old as 12; therefore for the sister to be twice as old as brother she will 24years when her brother is 12 years.

Or by calculation;

If 4 is the age for the brother, when the sister is 16, and y years will pass for the to be such that the sister is twice as old as the brother, then;

16 + y = 2(4 + y)

16 + y = 8 + 2y

16 - 8 = 2y - y

8 = y

Therefore, 8 years elapse before the sister is twice as old as the brother.

Sister will be: (16 + 8) = 24years

Brother will be: (4 + 8) = 12years

Aug 02, 2011 | Computers & Internet

Nov 09, 2010 | Health & Beauty

I have this same problem! Have you learned anything?

Mary in Rhode Island

Mary in Rhode Island

Aug 08, 2010 | Heating & Cooling

Three unknowns with three equasions:

cindy is 5 years older than alex. write it as c = a + 5

cindy is 7 years older than peter. write it as c = p + 7

The sum of their ages is 21. write it as c + a + p = 21

first solve for peters age in terms of alex's age.

c = p + 7 or

(a + 5) = p + 7 or

p = (a + 5) - 7 or

p = a - 2

substitute in and solve the equasion:

(a + 5) + a + (a - 2) = 21 or

3a + 3 = 21 or

3a = 24 or

a = 8

c = a + 5 or

c = 8 + 5 = 13

c = p + 7 or

p = c - 7 or

p = 13 - 7 = 6

cindy is 13, alex is 8 and peter is 6

This is called simultaneous equasions and will always work if you have the same number of unknowns as you have equasions (or relationships).

cindy is 5 years older than alex. write it as c = a + 5

cindy is 7 years older than peter. write it as c = p + 7

The sum of their ages is 21. write it as c + a + p = 21

first solve for peters age in terms of alex's age.

c = p + 7 or

(a + 5) = p + 7 or

p = (a + 5) - 7 or

p = a - 2

substitute in and solve the equasion:

(a + 5) + a + (a - 2) = 21 or

3a + 3 = 21 or

3a = 24 or

a = 8

c = a + 5 or

c = 8 + 5 = 13

c = p + 7 or

p = c - 7 or

p = 13 - 7 = 6

cindy is 13, alex is 8 and peter is 6

This is called simultaneous equasions and will always work if you have the same number of unknowns as you have equasions (or relationships).

Sep 20, 2009 | Puzzle Toys

Edwin is 14. Ruel is 7.

In 3 years Edwin will be 17. Edwin will be 10. (3*10 - 13 = 17)

Let x=Ruel's age now, and 2x=Edwin's age now.

2x+3=3(x+3)-13

2x+3=3x+9-13

2x+3=3x-4

2x+7=3x

7=x

If you are going to post these, the least you could do is rate them as Fixya. :-) Thanks!

In 3 years Edwin will be 17. Edwin will be 10. (3*10 - 13 = 17)

Let x=Ruel's age now, and 2x=Edwin's age now.

2x+3=3(x+3)-13

2x+3=3x+9-13

2x+3=3x-4

2x+7=3x

7=x

If you are going to post these, the least you could do is rate them as Fixya. :-) Thanks!

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