Why is it most logical to let x represent Dianna’s current age?
Accepted Solution
A:
let's say Diana is "x" years old today.
in 3 years, she's going to be " x + 3 " years old.
33 years ago, she was " x - 33 " old.
how much is 4 times that anyway? well 4(x-33), that's 4 times as 33 years ago her age.
now, we know in 3 years, x+3, she'll be "4 times as old as she was 33 years ago", 4(x-33), therefore, those amounts are equal then,
[tex]\bf \stackrel{\textit{3 years from now}}{x+3}~~=~~\stackrel{\textit{4 times as old as she was 33 years ago}}{4(x-33)}
\\\\\\
x+3=4x-132\implies 135=3x\implies \cfrac{135}{3}=x\implies 45=x[/tex]
why is it most logical to use "x" for her age today?
well, because 3 years from now is just x + 3 and 33 years ago is x - 33, 4 times that is 4( x - 33 ).