Jess uses her scanner to scan pages at the rate of $.09 per page. She decides to rent a scanner for $70 a year. The cost of scanning using the rented scanner is $.02 per page. Please help me write an inequality that can be used to calculate the number of pages that Jess should scan in a year so that the amount she pays for the rented scanner is less than the other scanner.
let n be the number of pages scanned
.02n + 70 ≤ .09n
70≤ .02n
or
.02n ≥ 70
n ≥ 3500
so 3500 pages is the break-even point
so anything greater than 3500 she should rent the scanner, at less than 3500 her old scanner will be better.
Maca
To write an inequality, let's assume that the number of pages Jess scans in a year is represented by the variable "x".
Let's first calculate the cost of scanning using her own scanner:
Cost using her own scanner = rate per page × number of pages
= $0.09 × x
= $0.09x
Next, let's calculate the cost of renting the scanner for a year:
Cost of renting scanner = rental cost + rate per page × number of pages
= $70 + $0.02 × x
= $70 + $0.02x
Now, to write the inequality, we want the cost of renting the scanner to be less than the cost of using her own scanner. Therefore, the inequality can be written as:
$70 + $0.02x < $0.09x
Simplifying the inequality:
$70 < $0.09x - $0.02x
$70 < $0.07x
Therefore, the inequality that can be used to calculate the number of pages Jess should scan in a year so that the amount she pays for the rented scanner is less than the other scanner is:
$70 < $0.07x