SOLUTION: The product of the two-digit number and its tens digit is 54. Find the number if the sum of the digits when added to the number gives a result of 36?

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Question 164855: The product of the two-digit number and its tens digit is 54. Find the number if the sum of the digits when added to the number gives a result of 36?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the tens digit be A, the ones digit be B.
The number is then A%2A10%2BB.
"The product of the two-digit number and its tens digit is 54."
1.%28A%2A10%2BB%29%2AA=54
1.10A%5E2%2BAB=54
"the sum of the digits when added to the number gives a result of 36"
2.A%2BB%2B%28A%2A10%2BB%29=36
2.11A%2B2B=36
From eq. 2,
2.11A%2B2B=36
2B=36-11A
B=18-%2811%2F2%29A
Subsitute this value into eq. 1 and solve for A.
1.10A%5E2%2BAB=54
10A%5E2%2BA%2818-%2811%2F2%29A%29=54
20A%5E2%2BA%2836-11A%29=108
20A%5E2%2B36A-11A%5E2=108
9A%5E2%2B36A-108=0
A%5E2%2B4A-12=0
%28A%2B6%29%28A-2%29=0
A negative value for A wouldn't make sense for this problem.
We'll only use the positive value.
A-2=0
A=2
From eq. 2,
B=18-%2811%2F2%29A
B=18-%2811%2F2%292
B=18-11
B=7
The two digit number is 27.
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Check your answer.
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"The product of the two-digit number and its tens digit is 54."
27%2A2=54
54=54
"the sum of the digits when added to the number gives a result of 36"
2%2B7%2B27=36
36=36
Both statements are true.
It's a good answer.