The sum of three numbers is 50. The product of the first two is 48 and the third is 12 more than the sum of the first two. What are the numbers?

Question

So I said let x= 1st # let y= 2nd number and let z=3rd number and then had x+y+z=50 and then xy=48 and then got confused on the last one so I said x+y=z+12

Answer 1

x + y + z = 50

 

xy=48

 

x + y + 12 = z------------ x +y -z =-12

 

x+y+z =50

x+y-z =-12

________________

2x+2y =38

x+y =19

 

x+y+z = 50

19+z= 50

z=31

 

x=19-y

xy=48

(19-y)y=48

19y-y² =48

 

y² -19y +48 =0

 

(y-16)(y-3)=0

y=16 or y=3

 

if y= 16 then x=3

 

if y= 3 then x=16

 

x=16, y=3 and z=31

or

 

x=3, y=16 and z=31