Question 163449
Kim is thinking of 2 numbers. The quotient is 4 and the difference is 27. What are the 2 numbers? 

ANSWER:
{{{x=1stnumber}}}
{{{x+1=2nd number}}}
1st condition: {{{x/(x+1)=4}}}, cross multiply
{{{4(x+1)=x}}}
{{{4x+4=x}}}
{{{4x-x=-4}}} -----> {{{3x=-4}}} ---> {{{cross(3)x/cross(3)=-4/3}}}
{{{x=-4/3}}}
Go back to the condition to check,
{{{(-4/3)/((-4/3)+1)=4}}}
{{{(-4/3)/(highlight((-4+3)/3))=4}}}, get LCD
{{{(-4/3)(3/-1)=4}}} ---> {{{(-4/cross(3))(cross(3)/-1)=4}}}
{{{(-4)(-1)=4}}}
{{{4=4}}}, oks!
Therefore, {{{(-4/3)=1stNumber}}}; {{{-1/3=2ndNumber}}} see above highlighted

Kylie and Ellie played basketball. Kylie scored half as many points as Ellie.
Together they scored 27 points. How many did each player score?
ANSWER:
{{{x}}}=score of Ellie
{{{(1/2)x}}}=score of Kylie
Total score={{{27pts}}}
Then, {{{x+(1/2)x=27}}}, EQN 1
{{{(2x+x)/2=27}}}, get LCD
{{{3x=54}}}, cross multiply
{{{cross(3)x/cross(3)=cross(54)18/cross(3)}}}
{{{x=18pts}}} ---------------> score of Ellie
{{{(1/2)18=9pts}}} ----------> score of Kylie
Check via EQN 1,
{{{18+9=27pts}}}, oks!
Thank you,
Jojo</pre>