what is the smaller number?

Question

The sum of two is 19, and their product is 78. What is the smaller number?

Answer 1

Hi Amy,

       Let x and y be the two numbers that we need then

 

x+y=19 and x*y=78 solve the second equation for y=78/x and sub in the first giving x+78/x=19 work on this equation to solve for x gives x² -19x+78=0 this factors into (x-13)(x-6)=0 so x=6 and y=19-x=13. For x=13 y=6.

 

The smaller of the two numbers is 6

 

Jim

Answer 2

Let x = one number and y = the other number

 

The sum of two numbers is 19: x + y = 19; so x = 19-y

 

Their product is 78: x*y = 78

 

Substitute 19-y in place of x in the second equation:

 

x*y = 78

(19-y)*y = 78             [Substituted 19-y in place of x]

19y - y² = 78

0 = y² - 19y + 78

0 = (y-13)(y-6)            [Factored the quadratic]

 

y = 13, 6

 

y can be either 13 or 6

 

If y=13, then x=19-y = 19-13 = 6. 

 

If y=6, then x = 19-6 = 13

 

x*y = 13*6 = 78

 

The smaller number is 6