SOLUTION: Please need your help and solution on this problem, <s>quadratic</s> problem. A number is one less than twice another number. The product of the two numbers is thrice the larger

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please need your help and solution on this problem, <s>quadratic</s> problem. A number is one less than twice another number. The product of the two numbers is thrice the larger      Log On


   

Question 984053: Please need your help and solution on this problem, quadratic problem.
A number is one less than twice another number. The product of the two numbers is thrice the larger number. Let y represents the smaller number. Which of the following equations can be used to find the two numbers?
Thank you very much in advance.
Mark
Found 2 solutions by macston, josgarithmetic:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
A number is one less than twice another number. The product of the two numbers is thrice the larger number. Let y represents the smaller number. Which of the following equations can be used to find the two numbers?
.
x and y are the two numbers
.
x=2y-1
xy=3x
%282y-1%29%28y%29=3%282y-1%29
2y%5E2-y=6y-3
2y%5E2-7y%2B3=0
%282y-1%29%28y-3%29=0
2y-1=0 OR y-3=0
2y=1 OR y=3
y=1%2F2 OR y=3
.
For y=1/2:
x=2y-1
x=2%281%2F2%29-1
x=1-1
x=0
ANSWER 1: The two numbers are 0 and 1/2.
.
For y=3:
x=2y-1
x=2%283%29-1
x=6-1
x=5
ANSWER 2: The two numbers are 5 and 3.
.
ANSWER 1 does not check, because x is not the larger number
So the only correct answer is ANSWER 2:
The two numbers are 5 and 3.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Hard to know where y fits being the smaller.
y and some other, x.
The product description: xy=3x, if y were the smaller number. This already brings very sharply how x and y are related.

xy=3x
%281%2Fx%29xy=%281%2Fx%293x
highlight%28y=3%29

First sentence: try both ways.
x=-1%2B2y OR y=-1%2B2x;

Already we have a value for y, and were given y%3Cx.
x=-1%2B2%2A3
x=-1%2B6
highlight%28x=5%29

Those values should be good, and the system was
highlight%28system%28xy=3x%2Cx=-1%2B2y%29%29.

Would the other equation work?
y%2B1=2x
x=%28y%2B1%29%2F2
x=%283%2B1%29%2F2
x=2------------No. This does not work. We were given that y%3Cx and we do not allow 3%3C2.