Let's solve each of these problems step-by-step.
### Question 14:
Mary must answer at least 20 problems correctly to get the grade she wants. She already knows she answered 5 problems correctly. We need to find out the remaining problems she needs to answer correctly, which we'll represent with [tex]\( c \)[/tex].
Since the total number of problems she answers correctly will be the sum of the problems she already answered (5) and the problems she needs to answer ([tex]\( c \)[/tex]), the inequality that describes this situation is:
[tex]\[ 5 + c \geq 20 \][/tex]
Thus, the best representation of this situation is:
B. [tex]\( 5 + c \geq 20 \)[/tex]
### Question 16:
Roberto started with [tex]$20. He bought a soccer ball that cost \( m \) dollars. After this purchase, he has less than $[/tex]5 left.
The amount of money Roberto has left after buying the soccer ball is calculated by subtracting the cost of the soccer ball ([tex]\( m \)[/tex]) from his initial amount ([tex]$20). This remaining amount must be less than $[/tex]5, so we write:
[tex]\[ 20 - m < 5 \][/tex]
Thus, the inequality representing this situation is:
A. [tex]\( 20 - m < 5 \)[/tex]
### Question 18:
The cost of renting a boat is [tex]$20 plus an additional $[/tex]2.50 per hour represented by [tex]\( x \)[/tex]. Millie wants to keep the total cost of renting the boat under [tex]$50.
The total cost of the boat rental is the fixed cost ($[/tex]20) plus the hourly cost ([tex]$2.50 for each hour \( x \)). Millie wants this total cost to be less than $[/tex]50, so we get:
[tex]\[ 20 + 2.50x < 50 \][/tex]
Thus, the inequality modeling this situation is:
D. [tex]\( 20 + 2.50x < 50 \)[/tex]
