Word Problem - Enough Info?

[dougp23]

Helping my 8th grade son out with his Pre-Algebra last night and he asks for help on this problem:

The weight of two sacks of potatoes is 168 grams. One-eighth of the weight of sack A and three-quarters of the weight of sack B is 76 grams.
Write an equation to find the weight of sack A, and solve for the weight of sack A.

Now, admittedly, it has been a while (about 30 years) since I had Algebra, but I was very good at it.
To me, the question is confusing. Is it saying "1/8 of sack A *PLUS* 3/4 of sack B equals 76 grams" or is it saying "both 1/8 of sack A and 3/4 of sack B weigh the same, 76 grams".

Either way, I could not begin to write an equation to solve it.

Can you help me out a bit? He had to skip it, so it won't count, but we were both a little mystified.

 

[Ishuda]

I think the 'and' means 'plus' as does the "the weight of two sacks" So. a is weight of sack A, b is weight of sack B and
a + b = 168
(1/8) a + (3/4) b = 76
For ease of use, multiply that last by 8 on both sides to get
a + b = 168
a + 6 b = 608

 

[dougp23]

Hey Ishuda,

That's sort of what I came up with too, but it still doesn't work...

1/8A + 3/4B = 76

Multiply by 8 to get A alone:

A + 6b = 608

So I still get nowhere....

 

[Ishuda]

Hey Ishuda,

That's sort of what I came up with too, but it still doesn't work...

1/8A + 3/4B = 76

Multiply by 8 to get A alone:

A + 6b = 608

So I still get nowhere....

what happens if you subtract one equation from the other?

 

[dougp23]

what happens if you subtract one equation from the other?

I guess I am nowhere as good as I think with Algebra.

2x + 3 = 7
I can figure out, easy. Subtract the 3 from both sides, divide by 2 to isolate X. X is 2.

But when you have something like

2x + 3y = 14

Where do you begin? You can't isolate either x or y.

So with my equation where we left off:

A + 6b = 608

I don't know what you mean by "subtract one equation from the other".
We could isolate A, by saying A = 608 - 6b. Great. We have no idea of what b equals, so solving for A is still not possible.

Am I missing something so incredibly basic, I am not "seeing the forest for the trees"?

 

[Steven G]

I guess I am nowhere as good as I think with Algebra.

2x + 3 = 7
I can figure out, easy. Subtract the 3 from both sides, divide by 2 to isolate X. X is 2.

But when you have something like

2x + 3y = 14

Where do you begin? You can't isolate either x or y.

So with my equation where we left off:

A + 6b = 608

I don't know what you mean by "subtract one equation from the other".
We could isolate A, by saying A = 608 - 6b. Great. We have no idea of what b equals, so solving for A is still not possible.

Am I missing something so incredibly basic, I am not "seeing the forest for the trees"?

What about the other equation?
You have:a + b = 168 and a + 6 b = 608. Subtract the two eqs and get 5b = 440. Double both sides and get 10b = 88. Solve for b. Not find a. How would you do that?

 

[dougp23]

Wow I feel old...I must be much older than I think, haha!

Thanks to both of you for your help. I don't ever remember doing a problem like this....of course, it was a long time ago.

Thank you again! If we see more of these on his math homework, I will know how to solve them!