Question

Why is it most logical to let x represent Dianna’s current age?

Answer 1

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,


`\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`

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 ).

works very well as a point of reference.

Answer 2

Diannas current age is what your being asked to find

Diannas age is the unknown in the problem

The given relatioships can be written in terms of diannas current age