Answer:
The inequality is [tex]55+10x\leq 105[/tex]
The greatest length of time Jeremy can rent the jet ski is 5 and Jeremy can rent maximum of 135 minutes.
Step-by-step explanation:
Given: Cost of first hour rent of jet ski is $55
Cost of each additional 15 minutes of jet ski is $10
Jeremy can spend no more than $105
Assuming the number of additional 15-minutes increment be "x"
Jeremy´s total spending would be first hour rental fees and additional charges for each 15-minutes of jet ski.
Lets put up an expression for total spending of Jeremy.
[tex]\$55+ \$ 10\times x[/tex]
We also know that Jeremy can not spend more than $105
∴ Putting up the total spending of Jeremy in an inequality.
[tex]\$ 55+\$10x\leq \$ 105[/tex]
Now solving the inequality to find the greatest number of time Jeremy can rent the jet ski,
⇒ [tex]\$ 55+\$10x\leq \$105[/tex]
Subtracting both side by 55
⇒ [tex]\$ 10x\leq \$50[/tex]
Dividing both side by 10
⇒[tex]x\leq \frac{50}{10}[/tex]
∴ [tex]x\leq 5[/tex]
Therefore, Jeremy can rent for [tex]60\ minutes + 5\times 15\\= 60\ minutes + 75= 135\ minutes[/tex]
Jeremy can rent maximum of 135 minutes.
