Gaussian Elimination: Translating text into equations

[Matty R]

Hello

I have a homework question regarding Gaussian Elimination, where I am supposed to use information in a block of text to get equations, and form an augmented matrix.

There are 4 unknowns, but I can only seem to get 3 equations and 3 "checks", to see if the values I get are correct.

Could anyone help me please?

I'm fine with Gaussian Elimination itself. I'm just having trouble translating the information into equations.

Homework Statement

Ann, Bea, Claire and Dawn have joint birthdays.
The sum of their ages is exactly 100 years.
The sum of Ann's and Dawn's ages is the same as the sum of Bea's and Claire's.
The difference between the ages of Claire and Bea is twice Ann's age.
When Claire is as old as Dawn is now, Bea will be twice as old as Ann currently is.
Claire is older than Bea.
How old is each person?

Homework Equations

The Attempt at a Solution

a + b + c + d = 100

a + d = b + c

a - b - c + d = 0

2a = c - b

2a + b - c = 0

c = d [tex]\Rightarrow[/tex] b = 2a

c > b

I end up with 4 unknowns in three equations, and apparently that means there are infinite solutions. I've been told a set of answers, and they fit all of the equations I've worked out, along with the "checks". I just can't seem to work out the fourth equation.

I'd be grateful for any and all help.

Thanks

 

[tiny-tim]

Hello Matty R!

When Claire is as old as Dawn is now, Bea will be twice as old as Ann currently is.
Claire is older than Bea.
…
c = d [tex]\Rightarrow[/tex] b = 2a

No, that doesn't mean anything, does it?

Hint: what will Bea's age be when Claire is as old as Dawn is now?

 

[HallsofIvy]

Hello

I have a homework question regarding Gaussian Elimination, where I am supposed to use information in a block of text to get equations, and form an augmented matrix.

There are 4 unknowns, but I can only seem to get 3 equations and 3 "checks", to see if the values I get are correct.

Could anyone help me please?

I'm fine with Gaussian Elimination itself. I'm just having trouble translating the information into equations.

Homework Statement

Ann, Bea, Claire and Dawn have joint birthdays.
The sum of their ages is exactly 100 years.
The sum of Ann's and Dawn's ages is the same as the sum of Bea's and Claire's.
The difference between the ages of Claire and Bea is twice Ann's age.
When Claire is as old as Dawn is now, Bea will be twice as old as Ann currently is.
Claire is older than Bea.
How old is each person?

Homework Equations

The Attempt at a Solution

a + b + c + d = 100

a + d = b + c

a - b - c + d = 0

2a = c - b

2a + b - c = 0

c = d [tex]\Rightarrow[/tex] b = 2a

c > b

"When Claire is as old as Dawn is now, Bea will be twice as old as Ann currently is.
Claire is older than Bea."
Claire will be as old as Dawn is now in d- c years. Bea's age then will be b+ (d- c) and that will be twice Ann's current age: b+ d- c= 2a or 2a- b+ c- d= 0.

I end up with 4 unknowns in three equations, and apparently that means there are infinite solutions. I've been told a set of answers, and they fit all of the equations I've worked out, along with the "checks". I just can't seem to work out the fourth equation.

I'd be grateful for any and all help.

Thanks

You have four equations:
The sum of their ages is exactly 100 years.
a+ b+ c+ d= 100

The sum of Ann's and Dawn's ages is the same as the sum of Bea's and Claire's.
a- b- c+ d= 0

The difference between the ages of Claire and Bea is twice Ann's age.
2a+ b- c= 0
("Claire is older than Bea" tells you that the difference between the ages of Claire and Bea is c- b, not b- c).

When Claire is as old as Dawn is now, Bea will be twice as old as Ann currently is.
2a- b+ c- d= 0

 

[Matty R]

Thanks for the replies.

Hello Matty R!

No, that doesn't mean anything, does it?

Hint: what will Bea's age be when Claire is as old as Dawn is now?

"When Claire is as old as Dawn is now, Bea will be twice as old as Ann currently is.
Claire is older than Bea."
Claire will be as old as Dawn is now in d- c years. Bea's age then will be b+ (d- c) and that will be twice Ann's current age: b+ d- c= 2a or 2a- b+ c- d= 0.

I'd never have got that. I completely see how to get it now, but I just couldn't understand it before.

I did get the set of answers I'd been told about.

Thanks again.