Sample quiz on linear relation word problems
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1. The cost of renting a hall is $\$300$ plus $\$50$ per person. If the cost is represented by $C$ and the number of people by $p$, an equation that models this scenario is $\cdots$?
   
   $p=300+50C$
   $C=300-50p$
   $C=300+50p$
   $p=300-50C$
   
2. A hall can accommodate a maximum of $100$ persons. The cost of renting the hall is $\$350$ plus an additional $\$45$ per person. What is the maximum amount the hall management can make any time they rent the hall?
   
   $\$4850$
   $\$4800$
   $\$4750$
   $\$4700$
3. If a physical situation is modelled by the equation $C=-2h+35$, the significance of the $-2$ in this equation is $\cdots$?
   
   $C$ increases by $2$ whenever $h$ increases by $1$
   $C$ increases by $2$ whenever $h$ increases by $2$
   $C$ decreases by $2$ whenever $h$ increases by $2$
   $C$ decreases by $2$ for every unit increase in $h$
4. A cellphone company charges a monthly fee of $\$25$ plus an additional $\$2$ per hour of international call. With a budget of $\$53$, how many hours of international call can a client make in a given month?
   
   $28$
   $14$
   $53$
   $26.5$
5. Cellphone company A charges $\$30$ per month plus an additional cost of $\$0.02$ for every minute of local call. Cellphone company B charges $\$25$ per month plus an additional cost of $\$0.025$ for every minute of local call. After how many minutes will their charges be equal?
   
   $1$
   $10$
   $100$
   $1000$
6. A certain worker's weekly wage is given by $W=20h$, where $h$ is the number of hours worked each week and $W$ is the wage. A possible interpretation of the $20$ in this equation is that $\cdots$
   
   the worker is paid $\$20$ every hour
   the worker works for $20$ hours each week
   the worker is paid $\$20$ every week
   the worker gets $\$20$ per day.
7. A marketer gets a fixed salary of $\$2500$. There is an additional pay of $\$12$ for every person the marketer convinces to buy a product. How many people does the marketer need to convince in order to earn $\$2800$ in a given month?
   
   $32$
   $30$
   $25$
   $24$
8. Consider the equation $d=-2t+10$. A physical situation modelled by this equation could be $\cdots$?
   
   a person walks at $10$ km/h and is moving away from a place $2$ km away
   a person walks at $10$ km/h and is moving towards a place $2$ km away
   a person walks at $2$ km/h and is moving away from a place $10$ km away
   a person walks at $2$ km/h and is moving towards a place $10$ km away.
9. A person runs towards a building that is $5$ km away. The person's speed is $1.5$ km/h. At any hour $t$, let the person's distance from the building be $d$. Then $\cdots$
   
   $d=5-1.5t$
   $d=5+1.5t$
   $5t-1.5$
   $5t+1.5$
10. Two tutoring companies -- Prolific Tutors and Pacific Tutors -- charge $C=150+20h$ and $C=120+25h$, respectively. $h$ is the number of hours of tutoring a student receives. After how many hours will their charges be equal?
    
    $5$ hours
    $6$ hours
    $24$ hours
    $25$ hours