SOLUTION: Find a 2 digit number less than 50 using these clues. It can be divided by 4 exactly. When 4 is added to it, it can be divided by 5 exactly?

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: Find a 2 digit number less than 50 using these clues. It can be divided by 4 exactly. When 4 is added to it, it can be divided by 5 exactly?      Log On


   



Question 956569: Find a 2 digit number less than 50 using these clues. It can be divided by 4 exactly. When 4 is added to it, it can be divided by 5 exactly?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It's a multiple of +4+ , so I can call
it +4n+ where +n+%3C=+12+
If +n+=+13+, then +4%2A13+=+52+
which is too much
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I am told:
+%28+4n+%2B+4+%29+%2F+5+ is a whole number
Call the whole number +k+
+4%2A%28+n+%2B+1+%29+%2F+5+=+k+
+n+%2B+1+=+%28+5%2F4+%29%2Ak+
+n+=+%285%2F4%29%2Ak+-+1+
-------------------
From above, I can say:
+%285%2F4%29%2Ak+-+1+%3C=12+
+%285%2F4%29%2Ak+%3C=+13+
+k+%3C=+%284%2F5%29%2A13+
+k+%3C=+52%2F5+
+k+%3C=+10+
-------------
+k+=+8+ gives me a whole number for +n+
+n+=+%285%2F4%29%2Ak+-+1+
+n+=+%285%2F4%29%2A8+-+1+
+n+=+9+
+4n+=+36+
The number is 36
----------------
check:
+36%2F4+=+9+
OK
+%28+36+%2B+4+%29+%2F+5+=+40%2F5+
+40%2F5+=+8+
OK

Answer by MathTherapy(10809) About Me  (Show Source):
You can put this solution on YOUR website!

Find a 2 digit number less than 50 using these clues. It can be divided by 4 exactly. When 4 is added to it, it can be divided by 5 exactly?
It’s divisible by 4, but when 4 is added to it, it’s divisible by 5 means that the number is a multiple
of 4 that when 4 is added to it, it becomes a multiple of 5. Therefore, the number will be 4 less than
a MULTIPLE of 4 & 5. Multiples of 4 & 5 that are less than 50 are: 20 and 40.
Number that's 4 less than 20: highlight_green%2816%29
Number that's 4 less than 40: highlight_green%2836%29