# Mum is 20 years older than Andrew and 24 years older than Anna. The three ages total 73.

#### LiseyDot05

##### New member
"MUM IS 20 YEARS OLDER THAN ANDREW, AND 24 YEARS OLDER THAN ANNE. THE THREE AGES TOTAL 73. HOW OLD IS MUM & HOW OLD IS ANDREW?"

Evening everyone. My little boy is trying to solve this problem. He got the correct answer (39, 19 & 15) but it was by guessing enough numbers until it was correct. Obviously not the way it was supposed to be done. ? Can anyone please give me a way to explain it to him in a way a 9 year old would understand??

Your son needs to define his variable.
Maybe he would choose to use M for Mum's age, A for Andrew's age and N for Anne's age
Translate MUM IS 20 YEARS OLDER THAN ANDREW using just M, A and N
Translate MUM IS 24 YEARS OLDER THAN ANNE using just M, A and N
Translate THE THREE AGES TOTAL 73 using just M, A and N.
Now try to solve that system of equations.
If your son still needs help, then he should respond showing how far he got.

"MUM IS 20 YEARS OLDER THAN ANDREW, AND 24 YEARS OLDER THAN ANNE. THE THREE AGES TOTAL 73. HOW OLD IS MUM & HOW OLD IS ANDREW?"

Evening everyone. My little boy is trying to solve this problem. He got the correct answer (39, 19 & 15) but it was by guessing enough numbers until it was correct. Obviously not the way it was supposed to be done. ? Can anyone please give me a way to explain it to him in a way a 9 year old would understand??
Most likely, this is not meant to be solved by actual algebra, as we would; it's even possible that guessing numbers is the expected way, at that age. Do you know what techniques the class has learned?

One way I've seen which is sort of an introduction to algebra, is to picture the three ages as strips of paper of appropriate lengths. We have one whose length is Mum's age; a second that is 20 less than that; and a third that is 24 less (and therefore 4 less than the second). Putting them together, the sum has to be 73.

So you might write Mum + (Mum - 20) + (Mum - 24) = 73, and then think about that.

Or, you might turn things inside out, and say that Andrew is 4 years older than Anne, and Mum is 24 years older than Anne, and label three strips as Ann, (Ann + 4), and (Ann + 24). Putting those together, you have three Annes, and 28 more, making a total of 73. Then think about that.

Algebra is just a way to do the same thinking using symbols instead of (imagined) objects.

He needed to show working out so he did:

73 + 24 + 20 = 117

117 ÷ 3 = 39

39 - 20 = 19 (Andrew)

39 - 24 = 15 (Anne)

Has he just had luck on his side again?

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Has he just had luck on his side again?
Looks like a good solution to me (especially if you change division to subtraction in computing Anne's age).
I can see an explanation like this:
1. 73 is the Mom+Andrew+Anne
2. Since Mom is 20 year older than Andrew then 73 + 20 is Mom + Mom + Anne
3. Since Mom is 24 years older than Anne then 73 + 20 + 24 is Mom+Mom+Mom = 3 x Mom = 117
Would this make sense to your son?

Looks like a good solution to me (especially if you change division to subtraction in computing Anne's age).
I can see an explanation like this:
1. 73 is the Mom+Andrew+Anne
2. Since Mom is 20 year older than Andrew then 73 + 20 is Mom + Mom + Anne
3. Since Mom is 24 years older than Anne then 73 + 20 + 24 is Mom+Mom+Mom = 3 x Mom = 117
Would this make sense to your son?
Sorry, the division symbol was my poor typing!

He needed to show working out so he did:

73 + 24 + 20 = 117

117 ÷ 3 = 39

39 - 20 = 19 (Andrew)

39 - 24 = 15 (Anne)

Has he just had luck on his side again?
Looks very good; not luck at all.

I would add words (like @blamocur's) to explain the reason for each computation; too many students think that mathematical thinking can't include words! But reading words into what I see, this appears to be essentially what I hoped he would come up with when I said "think about that" for my first suggestion.

As always, thank you for all of your help, everyone.