One number is 8 greater than another. The product of the numbers is 105. Find the numbers.

Question

Help me please 

Answer 1

Surely you must have seen problems of this kind begin by saying LET x be one number; then another is x+8 (eight more than first number).

 

Now that's established, the product of these is 105.  That means, in our algebraic system, x(x+8) = 105.

 

Using the wonderful distributive property (or law); x²+8x = 105.

 

We can put all terms on one side to get a quadratic equation (& then hope that we can factor it):

x²+8x-105=0

(x+15)(x-7) = 0.

 

Using the beloved Zero Product Property, we get two answers; x = 7 or x = -15.

 

We have two solutions, therefore: larger number is 15, smaller number is 7, OR

larger number is -7, smaller number is -15.

Answer 2

n, n+8

n(n+8)=105

n^2+8n=105

n^2+8n-105=0

(n+15)(n-7)=0

n-7=0

n=7

n+8=15

7 and 15 are the numbers

another solution...

 

105=3*5*7=(3*5)*7=15*7 answer