Question

One number is 50 more than twice another. Their product is 50 more than twice their sum. Find the numbers

Answer 1

let the numbers be x and y
y = 2x + 50
x*y = 50 + 2(x + y)
more than means add
twice means 2 times
product means multiply and sum means add

you have 2 equations you need to solve simultaneously
hint 2x = 2x
solve for x substitute in an original to find y

Answer 2

im trying to work this

Answer 3

I did it twice and got x = 3 so that means y = 56

Answer 4

what do you have?

Answer 5

I have to come up with four numbers. A set of lower values and higher values set

Answer 6

I am thinking that I used x*y also need to use (-x)*(-y)
absolute value somewhere

Answer 7

I am thinking use when x > y need to consider x< y

Answer 8

what if any values do you have?

Answer 9

@mathstudent55 do you mind helping?

Answer 10

y = 2x + 50
x*y = 50 + 2(x + y)
---------------------------
x(2x + 50) = 50 + 2(x + (2x + 50) )
2x^2 + 50 x = 50 + 2( 3x +50)
2x^2 + 50 x = 50 + 6x + 100
2x^2 + 50 x = 6x + 150
2x^2 + 50 x - 6x = 150
2x^2 + 44x - 150 = 0
x^2 +22x - 75 = 0
( x + 25 ) (x - 3) = 0 ****
x = - 25 OR x = 3

@chris @triciaal

Answer 11

x = - 25 OR x = 3
If x = - 25, then y = 2*(-25) + 50 = 0
Result One: ( - 25, 0 )
----> If x = 3, then y = 2*(3) + 50 = 56
Result Two: (3, 56)

Answer 12

@Directrix thanks when y = 0 then 0-2x= 50 so x = -25
by the way equating the (2x) or the (50) was much easier and faster than substitution for y

Answer 13

"Fast is fine but accuracy is everything." ~Wyatt Earp

The reason I attempted to help in this thread was to assist in finding the missing two answers, the absence of which was mentioned above.

Result One: ( - 25, 0 )
----> If x = 3, then y = 2*(3) + 50 = 56
Result Two: (3, 56)