# How do you translate word phrases to algebraic expressions: the quotient of a number and 7 added to twice the number is greater than or equal to 30?

Feb 26, 2017

The statement is a bit ambiguous:

$\frac{x}{7} + 2 x \ge 30 \text{ or } \frac{x}{7 + 2 x} \ge 30$

#### Explanation:

This is a good example of how the absence of any punctuation leads to an ambiguous statement:

Call 'the number' $x$

Look at the key words:

"quotient" is the answer to a division: look for the word 'and'

"twice the number" means multiply by 2, so $2 \times x = 2 x$

"greater than or equal" indicates an inequality: $\ge$

$\textcolor{b l u e}{\text{The quotient of a number and 7,")color(red)(" added to twice the number,")color(limegreen)(" is greater than or equal to 30}}$
$\textcolor{b l u e}{x \div 7} \textcolor{red}{+ 2 x} \textcolor{\lim e g r e e n}{\ge 30} = \frac{x}{7} + 2 x \ge 30$

The sentence above is different from

$\textcolor{b l u e}{\text{The quotient of a number and,")color(red)(" 7 added to twice the number,")color(limegreen)(" is greater than or equal to 30}}$
$\textcolor{b l u e}{x \div} \textcolor{red}{\left(7 + 2 x\right)} \textcolor{\lim e g r e e n}{\ge 30} = \frac{x}{7 + 2 x} \ge 30$

It really is about making the intention as clear as possible.
In the absence of any punctuation, I would opt for the first.