SOLUTION: I have been trying to figure out how this is set up but I am confused. So far I not sure if this is the right set up: n-4=96 Word Problem: The product of a number and 4 less

Question 88508: I have been trying to figure out how this is set up but I am confused. So far I not sure if this is the right set up: n-4=96
Word Problem:
The product of a number and 4 less than the number is 96. Find the number.
Found 3 solutions by bucky, Earlsdon, ptaylor:
Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
Call one missing number "n". Then the other missing number is "n-4".
.
The product of those two numbers is n times the quantity n - 4, and that product is 96.
.
In equation form this is:
.

.
Multiply out the left side and you get:
.

.
Get this quadratic equation into standard form by subtracting 96 from both sides. When you
do this subtraction, the equation becomes:
.

.
The left side can be factored and when you do that the equation is:
.

.
This equation will be true if either of the factors on the left side equals zero because zero
times anything is zero. So we can say that either
.

.
which after adding 12 to both sides becomes
.
or else
.

.
which after subtracting 8 from both sides becomes
.
So there are two possible answers for n. Either n = 12 or n = -8.
.
Let's check them out. If n is 12 then n minus 4 is 8. And 12 times 8 is 96. Therefore,
n = 12 checks out.
.
If n = -8, then n minus 4 is -8 - 4 = -12. And -8 times -12 equals +96 so it checks out too.
.
Both answers check out. So, again, n is either +12 or -8.
.
Hope this helps you to understand the problem.
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Let the required number be n.
The product (X) of a number (n) and 4 less than the number (n-4) is (=) 96.

Subtract 96 from both sides.
Solve this quadratic equation by factoring.
Apply the zero products principle.
or
So...n = 12 or n = -8 Discard the negative solution.
The number is 12.
Check:

Answer by ptaylor(2198)   (Show Source): You can put this solution on YOUR website!
Let x=the number
4 less than the number is x-4
the product of the number and 4 less than the number is x(x-4) and we are told that this equals 96, so---
x(x-4)=96 get rid of parens
x^2-4x=96 subtract 96 from both sides
x^2-4x-96=0 quadratic in standard form and it has factors
(x-12)(x+8)=0
x=12
and
x=-8
CK for x=12
12(12-4)=96
12*8=96
96=96-----------ok
Ck for x=-8
-8(-8-4)=96
(-8)(-12)=96
96=96
So both values for x satisfy the problem

Hope this helps----ptaylor

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