Age word problem - please help

[Rengoku0510]

Hello, I am stuck solving this question and would like to get some help.

Kaye and Lyn are twins, and the sum of their age is equal to three times the age of Dave, who is half as old as Keith. The average of the four children is six.

Use this information to write down an equation.

I could only figure out Kaye and Lyn would be written as 2x

 

[Harry_the_cat]

Kaye and Lyn are twins ... let each of their ages be x, then the sum of their ages is x + x = 2x, as you said.

the sum of their age is equal to three times the age of Dave ... let Dave be d years old, then 2x = 3d, so d = \(\displaystyle \frac{2}{3}\)x

Dave, who is half as old as Keith ... let Keith be k years old, then d=\(\displaystyle \frac{1}{2} k\), so k = 2d = .... in terms of x.

Can you finish it off?

 

[Otis]

Use this information to write down an equation

Hi Rengoku. Is writing an equation showing the average the only thing they've asked you to do, or do you also need to find the ages?

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[Rengoku0510]

Hi Rengoku. Is writing an equation showing the average the only thing they've asked you to do, or do you also need to find the ages?

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Hi Otis, yes they asked me to find their ages in the second question.

 

[Otis]

yes they asked me to find their ages in the second question.

Hi. Thanks for the clarification. (In the future, please post the entire exercise, so we can see all of the given information. And be sure to check out the forum guidelines, if you haven't already. Thanks!)

I'd asked because Harry the Cat's symbols for Dave's and Keith's name (d and k) would have been okay as is, if you didn't need to solve the equation.

Now it's clear that you do need to solve it. Therefore, you want to construct an equation that contains only one variable. (Otherwise, you wouldn't be able to find all three values x,d,k.) That's why Harry used the given relationship 2x=3d to express Dave's age in terms of x. Like this: d=(2/3)x

Do you understand how Harry set up the equation 2x=3d ?

Do you understand how Harry went from 2x=3d to d=(2/3)x ?

If so, try to write Keith's age using x. Start with the given relationship d=(1/2)k and make a substitution for d, then solve for k. When all ages are expressed in terms of x, the equation showing that the average age is 6 can be solved for x. Once we know x, we can find d (for example) using our equation d=(2/3)x, and so on.

We need to know what you're thinking, so please show your attempt at answering Harry's question or explain where you get confused.

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[Rengoku0510]

Hello guys,

I didn't think Dave and Keith's age would be written as fractions!!
I looked at my notes from yesterday and realised I was very close to get the equations for Dave and Keith, I just needed to simplify and express them in terms of X. (I was writing like 2x =Dave•3)

Once I understood how they would be written down it was easy to find the answers.

Thank you for your instructions and I will post the entire exercise next time

 

[Otis]

I didn't think Dave and Keith's age would be written as fractions!

Hi again. The ages are not actually written as fractions, Rengoku. They're written as x, d and k. The fractions appear when we compare ages.

In other words, expressing a Whole number as a fractional amount of a different Whole number doesn't mean the number is a proper fraction. For example, if H is age 10 (think 5+5) and K is age 15 (think 5+5+5), then their age relationship is H=(2/3)K. The numbers H and K remain Whole. The fraction 2/3 is not part of either age; it's just part of their relationship: 10 is two-thirds of 15.

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