A positive number is 3 times another number.If we add 2 to the larger and 5 to the smaller, then one of them becomes 2 times the other.Find the smaller number.
Accepted Solution
A:
Answer:The smaller number can be 8 or [tex]\frac{1}{5}[/tex].Step-by-step explanation:Consider the provided information.let the larger number is x and the smaller number is yA positive number is 3 times another number.[tex]3y=x[/tex]If we add 2 to the larger and 5 to the smaller, then one of them becomes 2 times the other.Case I: If 2nd number is 2 times to the first number.[tex]x+2=2(y+5)[/tex]Substitute the value of x.[tex]3y+2=2y+10[/tex][tex]y=8[/tex]Now substitute the value of y in [tex]3y=x[/tex][tex]3(8)=x[/tex][tex]x=24[/tex]Therefore, the smaller number is 8.Case II: If 1st number is 2 times to the second number.[tex]2(x+2)=y+5[/tex]Substitute the value of x.[tex]2(3y+2)=y+5[/tex][tex]6y+4=y+5[/tex][tex]5y=1[/tex][tex]y=\frac{1}{5}[/tex]Therefore, the smaller number is [tex]\frac{1}{5}[/tex].