1. If the same number is added to the numerator and subtracted from the denominator of 23/12, the resulting fraction is equivalent to the reciprocal of 2/3. What is the number?
Accepted Solution
A:
Answer:The number is -2Step-by-step explanation:step 1Find the reciprocal of 2/3Remember that when multiply a number by its reciprocal, the result is 1soThe reciprocal of 2/3 is 3/2step 2Let x-----> the number added to the numerator and denominator[tex]\frac{23+x}{12-x}=\frac{3}{2}[/tex]Solve for x[tex]2(23+x)=3(12-x)\\46+2x=36-3x\\2x+3x=36-46\\5x=-10\\x=-2[/tex]step 3verify[tex]\frac{23+x}{12-x}[/tex]substitute x=-2[tex]\frac{23-2}{12+2}[/tex][tex]\frac{21}{14}[/tex]Simplify[tex]\frac{3}{2}[/tex] ----> is okthereforeThe number is -2