How much do you pay each hour? Should we add any flat rates?
Rule in Words: 5 more than the product of 9 and a number n Rule as an Algebraic Expression: 9n+5
Practice makes perfect
We are asked to write this situation as a rule in words and as an algebraic expression. Let's write it in words first and use that to create our algebraic expression.
Rule in Words
Renting a bicycle costs $9 every hour. This means that we can find the total cost of the bicycle rental, not including the cost of the helmet, by multiplying 9 by the number of hours we are using it. Let's look at a few examples of how this works.
Number of Hours
Cost Calculation
Cost for Rental
1
$9* 1
$9
2
$9* 2
$18
3
$9* 3
$27
Now, we also have to include the cost of renting a helmet. The helmet is a flat rate of $5 no matter how long we are using it. Let's include this in our table.
Number of Hours
Cost Calculation
Cost for Rental
Plus Helmet Rental
Total Cost
1
$9* 1
$9
$9+ $5
$14
2
$9* 2
$18
$18+ $5
$23
3
$9* 3
$27
$27+ $5
$32
We can represent addition as more than and multiplication as the product of.
Therefore, we can write this rule in words.
5 more than the product of9 and a numbern.
Rule as an Algebraic Expression
To write the rule as an algebraic expression, we first need to assign a variable to the number of hours because it is the part that changes. We can say that an arbitrary number n represents the number of hours we rent the bicycle.
5 more than the product of 9 and a numbern
9 * n + 5
⇕
9n+5
