SOLUTION: I don't really know what category this problem falls under. It is confusing as to how to set up the problem. Please help. The difference of two numbers is 91. The second is 5 le

Algebra ->  Average -> SOLUTION: I don't really know what category this problem falls under. It is confusing as to how to set up the problem. Please help. The difference of two numbers is 91. The second is 5 le      Log On


   

Question 81634: I don't really know what category this problem falls under. It is confusing as to how to set up the problem. Please help.
The difference of two numbers is 91. The second is 5 less than 5 times the first. What are the two numbers?
Found 2 solutions by renevencer22, chitra:
Answer by renevencer22(21) About Me  (Show Source):
You can put this solution on YOUR website!
x - y = 91
y = 5*x - 5

x - (5*x - 5) = 91
-4*x + 5 = 91
x= 86/(-4) = -21.5
y = 5*x - 5 = -112.5

Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
Let a and b be the two numbers.

Given that the difference of a and b is 91

Also, given that the second is 5 less than 5 times the first.


So, b = 5a - 5


Hence, a - (5a - 5) = 91

a - 5a + 5 = 91

-4a + 5 = 91

-4a = 91 - 5

- 4a = 86

==> a = -%2886%2F4%29

==> a = - 43%2F2

Hence, the second number is:


5a - 5 = 5-43%2F2 - 5

[-215%2F2 - 5]

[%28-215+-+10%29%2F2]

==> %28-225%2F2%29

Hence, b = - %28225%2F2%29


verification:

So hence, substituting for the value of "a" in the equation, we get:

- 43%2F2 - [ 5(-43%2F2) - 5]

- 43%2F2 + [215%2F2 + 5]

Taking LCM, we get:

[%28-+43++%2B+215+%2B+10%29%2F2]

[182%2F2]


==> 91 = RHS.

Hence, the solution.