Hi there!
Call the ones "O" and the fives "F".
Let's set up two equations:
Based on the total mass of the notes:
O + F = 108
Based on the difference between masses:
O - F = 26
Now, let's add the two equations together:
O + F + O - F = 108 + 26
Simplify:
2O = 134
Divide by 2:
O = 67
To get F, use the second equation we made:
67 - F = 26
F = 67-26
F = 41
$1 notes: 67 grams
$5 notes: 41 grams
Let me know if you have any questions. If not, thanks for pressing "Accept".
-Scott
Is there a simplier way to get the answer. My daughter is just a fifth grader. She hasn't done a lot with algebra. If not, can you explain the O+F+O-F=108=26. She isn't sure how you got the 20.
Oh, I hadn't realized what grade this was for (when I first opened this, the "Fifth Grade" wasn't showing).
If you want to solve this without algebra (which I'm guessing you want), you can do it like this...
First divide the 108 by 2, so that we have half the notes as each type:
108/2 = 54
Now, remember that the difference between them has to be 26. Half of that difference has to be above and half as to be below. Let's divide the 26 by 2:
26/2 = 13
Add and subtract that with 54:
54+13 = 67
54-13 = 41
That's the non-algebra way to get 67 and 41. All you are doing is splitting both the total weight in half, and then splitting the weight difference in half.
Please do let me know if you have any other questions, or if your daughter is still confused. You don't have to accept until you understand this completely.
Scott
MIT Graduate
College degree in math... proficient in all levels -- from algebra to calculus
Glad to help :)