A and B together have $240. If A gives B $20, A will have 3 times as much money as B. How much money did A and B both have respectively?

A had $200 and B had $40

If you’re Taiwanese you’re math is supposed to be decent. If you’re an English teacher, white collar, or an engineer you’re supposed to be college educated. What gives with the jr. high math problem? the answer (A started with 200)

$240 total

A gives $20 to B

B have S60 after receiving this $20

A have $180 left

$180 is 3x more than 60

A+B = 180 + 60 =240

Appreciate the answers but forgot to ask if you could include the solution. It’s for my daughter’s grade 6 homework and she needs to demonstrate how she came to the answer.

Sincerely,

bigsyd

3a + (b+20) = 240…or something similar…never mind… :aiyo:

Would this make sense:

3x(B+20)=240

B+20=240/3

B=80-20

B=60

A=3B

A=3x60

A=180

This is what they currently have. Originally A would have had 180 + 20 = 200 and B would have had 60 - 20=40

Does that look mathematically sound?

I guess, but according to your formula it should be 3x + (x+20) = 240 with A=3x and B=x+20… with 3x(B+20)=240 the x can’t disappear on its own…you have 2 unknowns…in case the teacher is a nit-picker…it’s pretty sad me trying to give math advice…

After OriginalA gives OriginalB $20, NewA has three times as much as NewB. The total is always 240.

NewA= 3x NewB

3x NewB + NewB = 240

4x NewB = 240

NewB = 60

OriginalB = NewB - 20 = 60 - 20 = 40

OriginalA = 200

You are welcome!

Trust me, it is even sadder for me as a father to have to ask for it.

So what about this:

3(B+20)=240

B+20=240/3

B+20=80

B=80-20

B=60

A=3B

A=180

Better if they would teach common sense (cents).

He’s typing not speaking.

Let’s start after the giving of the $20.

We know that A = 3B. We also know that A + B = 240.

A + B = 240 can be rewritten as

3B + B = 240

or, 4B = 240

So, B=60. And thus Then, A = 3 x 60 = 180.

Now, let’s look at the amounts before the giving of $20. This means A originally had 180 + 20 = 200, and B originally had 60 - 20 = 40.

Solution:

A originally had $200

B originally had $40

That’s math for you! (Yes, math, with no “s”. It’s not called “mathsematic”!)

A + B = 240 … A = 240 - B

A-20 = 3(B+20)… A -20 = 3B + 60 … A = 80 +3B

--------by elimination--------------

A = 240 - B subtract

A = 80 + 3B

0 = 160 - 4B… 4B = 160…B = 40

put B back in the original A = 200

-----by substitution-------------

240 - B = 80 + 3B …240 = 80 + 4B …160 = 4B …B =40

put B back in the original A = 200

Edit* To OP, if you want your daughter to learn from this, it is more important that she understand how to apply this to every problem of this type. While this is trivial and can be solved in your head in a couple of seconds, I’m pretty sure whats being taught here is simultaneous equations. The principle is simple, first write the two equations, here A +B = 240 and A-20 = 3(B+20). Then rearrange for A or B, doesn’t matter which, whatever is easier, then you choose to solve the equation either by elimination or substitution, either one is fine, and finally put your answer back to the original and recheck your answers.

Let’s start after the giving of the $20.

We know that A = 3B. We also know that A + B = 240.

A + B = 240 can be rewritten as

3B + B = 240

or, 4B = 240

So, B=60. And thus Then, A = 3 x 60 = 180.

Now, let’s look at the amounts before the giving of $20. This means A originally had 180 + 20 = 200, and B originally had 60 - 20 = 40.

Solution:

A originally had $200

B originally had $40

That’s math for you! (Yes, math, with no “s”. It’s not called “mathsematic”!)[/quote]

Thanks Chris,

That makes perfect sense. You need to rearrange it so you express one of the unknowns in terms of the other. That way you are only solving for one unknown. I kept on coming unstuck when I realized you couldn’t solve for two unknowns.

Mick’s explanation is also neat, although it might be a bit more difficult for a sixth grader to understand. Perhaps, instead of doing the subtraction bit (which I am sure she will tell me her teacher hasn’t taught her, yet) it might be easier to do it thus:

[quote]A + B = 240 … A = 240 - B

A-20 = 3(B+20)… A -20 = 3B + 60 … A = 80 +3B [/quote]

If A=80+3B and we know that A+B=240,

then

80+3B+B=240

80+4B=240

4B=160

B=40

Same answer. Different route.

Thanks for everyone’s input. I really appreciate it.

bigsyd

maths is short for math(ematic)s, me old China. But I can’t fault your algebra.