So let’s leave statistics for a while and return to algebra. This post will be a bit more basic but it illustrates a skill needed when converting word problems to equations. First, a couple of definitions:
An Expression in algebra is basically anything you can write down in algebra without the “equal” symbol. You can think of an expression as either side of an equation. Examples are
\[{x}^{2}\hspace{0.33em}{+}\hspace{0.33em}{3}{x}\hspace{0.33em}{-}{1}{,}\hspace{0.33em}{2}{a}\hspace{0.33em}{+}\hspace{0.33em}{3}{b}{,}\hspace{0.33em}\frac{{x}\hspace{0.33em}{+}\hspace{0.33em}{1}}{{x}\hspace{0.33em}{-}\hspace{0.33em}{1}}{,}\hspace{0.33em}{5}\]They can be complex with more than one unknown or as simple as a number.
An Equation in algebra is two expressions with an “equal” symbol between them. Examples are
\[\begin{array}{l}{{x}^{2}\hspace{0.33em}{+}\hspace{0.33em}{3}{x}\hspace{0.33em}{-}{1}\hspace{0.33em}{=}\hspace{0.33em}{2}{a}\hspace{0.33em}{+}\hspace{0.33em}{3}{b}}\\{\frac{{x}\hspace{0.33em}{+}\hspace{0.33em}{1}}{{x}\hspace{0.33em}{-}\hspace{0.33em}{1}}\hspace{0.33em}{=}\hspace{0.33em}{5}}\\{{y}\hspace{0.33em}{=}\hspace{0.33em}{7}}\end{array}\]So let’s look at creating expressions. In what follows, I am going to write an english phrase and follow that with the equivalent algebraic expression.
Double a number: 2x
One more than a number: x + 1
Half of a number: x/2
Seven less than triple a number: 3x -7
Take 5 more than a number then double it: 2(x + 5)
Other letters can be used to show an unknown number, but x is mostly used. Sometimes more that one unknown is needed:
Cost of 3 pears that cost p each: 3p
Cost of 7 apples that cost a each: 7a
Total cost of the above fruit: 3p + 7a
The individual price 3 people pay at a restaurant if they split the bill: C/3
The total number of pencils in a classroom if each girl has 3 pencils and each boy has 2: 3g + 2b
It is usually a good practice to break down a word problem and write down the expressions first before generating an equation.
Let’s look at creating equations in my next post.