SOLUTION: A 2-digit number is 52 greater than the product of its digits. If the ten's digit is 4 larger than the unit's digit, find the number.

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Question 1111812: A 2-digit number is 52 greater than the product of its digits. If the ten's digit is 4 larger than the unit's digit, find the number.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
Just solved and explained under this link
https://www.algebra.com/algebra/homework/word/numbers/Numbers_Word_Problems.faq.question.1111809.html

https://www.algebra.com/algebra/homework/word/numbers/Numbers_Word_Problems.faq.question.1111809.html


Do not post it again.


Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Two parts of the description:
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2-digit number is 52 greater than the product of its digits.
--
t for TENS, u for ONES
10t%2Bu=52%2Btu
10%28u%2B4%29%2Bu=52%2Bu%28u%2B4%29
..
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and

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If the ten's digit is 4 larger than the unit's digit,
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This second part means that the two-digit number will be one of those among 51, 62, 73, 84, 95.

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10t%2Bu=52%2Btu
10%28u%2B4%29%2Bu=52%2Bu%28u%2B4%29
10u%2B40%2Bu=52%2Bu%5E2%2B4u
u%5E2%2B4u%2B52=11u%2B40
u%5E2-7u%2B12=0
highlight_green%28%28u-3%29%28u-4%29=0%29
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u could be either system%283%2COR%2C4%29.

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BOTH of these will work in the original first-part equation, of 10t%2Bu=52%2Btu;
system%28highlight%2873%29%2COR%2Chighlight%2884%29%29