There are two numbers

Question

there are two numbers with the following properties. 1) one number is 7 more than the other number 2) The product of two numbers is 13 less than their sum. Which of the following represents possible values of the two numbers

A. 3, -4

B. 2, 9

C. -3, -10

D. -2, 5

Answer 1

x and x+7 are the numbers

x(x+7)=x+(x+7)-13

x^2+7x=2x-6

x^2+7x-2x+6=0

x^2+5x+6=0

(x+2)(x+3)=0

x+2=0, x=-2

x+3=0, x=-3

-2 and 5 is one possibility

-3 and 4 is another

which one/ones work ?

they both work so D. is the answer

Answer 2

Itzel,

let the other number x, and then the one number is x + 7

Their product is x(x + 7), and their sum is x + (x + 7) = 2x +7

So the equation is x(x + 7) + 13 = 2x + 7

x² + 7x + 13 = 2x + 7

x² + 5x + 6= 0

(x +2)(x + 3) = 0

x = -2 and x = -3

the answers in each case: -2 and -2 +7=5 and -3 and 4, so answer D is possible.