Question 984053
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?
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x and y are the two numbers
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{{{x=2y-1}}}
{{{xy=3x}}}
{{{(2y-1)(y)=3(2y-1)}}}
{{{2y^2-y=6y-3}}}
{{{2y^2-7y+3=0}}}
{{{(2y-1)(y-3)=0}}}
{{{2y-1=0}}} {{{OR}}} {{{y-3=0}}}
{{{2y=1}}} {{{OR}}} {{{y=3}}}
{{{y=1/2}}} {{{OR}}} {{{y=3}}}
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For y=1/2:
{{{x=2y-1}}}
{{{x=2(1/2)-1}}}
{{{x=1-1}}}
{{{x=0}}}
ANSWER 1: The two numbers are 0 and 1/2.
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For y=3:
{{{x=2y-1}}}
{{{x=2(3)-1}}}
{{{x=6-1}}}
{{{x=5}}}
ANSWER 2: The two numbers are 5 and 3.
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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.