Digital Game
Algebra
Level
pending
There is a number, the second digit of which is smaller than its first digit by 4, and if the number was divided by the digits sum, the quotient would be 7. Can you find the number?
The answer is 84.
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1 solution
You can write the number as (10a + b), with 'a' being the first digit and 'b' being the second one. With this notation, we get the following system:
a - b = 4
(10a + b)(a+b) = 7
The first equation implies that b = a-4, and by using substitution we get:
(10a + a - 4)/(a + a - 4) = 7
(11a - 4) / (2a -4) = 7
11a - 4 = 7(2a - 4)
11a-4 = 14a - 28
3a = 24
a = 8
By using the first equation once again, we get that 8 - b = 4, so b = 4
So the number is 84.