23+23+⋯+23⏟A copies of 23=45+45+⋯+45⏟B copies of 4520≤A+B≤24A+B=?I have A copies of 23 on...

Katherine Walls

Katherine Walls

Answered

2021-12-16

23+23++23A copies of  23=45+45++45B copies of  45
20A+B24
A+B=?
I have A copies of 23 on the left-hand side of the equality, and B copies of 45 on the right. In total, I've written down between 20 and 24 fractions. Exactly how many fractions are there?

Answer & Explanation

Karen Robbins

Karen Robbins

Expert

2021-12-17Added 49 answers

Well you have
23A=45BB=56A
so
A+B=116A
Since A+B is an integer and is between 20 and 24, we must have that
A+B=116(12)=22
Wendy Boykin

Wendy Boykin

Expert

2021-12-18Added 35 answers

For both fractions I made their denominator equal, so:
23=1015  and  45=1215.
The smallest multiple they have on common is 60, so to get equality this means we need 6 times 23 and 5 times 45. Hence the answer must be a multiple of 11, so the answer is 22.
RizerMix

RizerMix

Expert

2021-12-29Added 437 answers

We have
23A=45B;
which gives
B=5A6
which says that A is divided by 6.
In another hand,
2056A+A24
or
12011A14411
or
101011A13111
which gives
A=12,
B=10
and
A+B=22.

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