Question

linear equations
classwork: real - world
scenarios. name
instructions: choose the best answer for
each multiple - choice question.

1. a plumber charges a flat fee of $75 to

come to your house and $60 per hour for
labor. which equation represents the total
cost (y) for x hours of work?
a. $y = 75x + 60$
b. $y = 60x + 75$
c. $y = 135x$
d. $y = 60x - 75$

1. a local gym charges a $50 sign - up fee

and monthly dues of $30. which equation
represents the total cost (y) after x
months?
a. $y = 30x + 50$
b. $y = 50x + 30$
c. $y = 80x$
d. $y = 30x - 50$

1. an online bookstore charges $15 per

book and a flat shipping fee of $5 per
order. which equation represents the total
cost (y) for x books?
a. $y = 5x + 15$
b. $y = 15x + 5$
c. $y = 20x$
d. $y = 15x - 5$

1. a taxi service charges $3.50 per mile

plus a $2.00 base fee just to start the ride.
which equation models this?
a. $y = 2x + 3.50$
b. $y = 3.50x + 2$
c. $y = 5.50x$
d. $y = 3.50x$

1. you have $100 in your savings account

and you deposit $20 every week. which
equation represents your balance (y) after
x weeks?
a. $y = 100x + 20$
b. $y = 120x$
c. $y = 20x + 100$
d. $y = 20x - 100$

1. which scenario best describes the

equation $y = 10x + 15$?
a. a car wash charges $10 for a wash and
$15 for a wax.
b. a music app costs $15 per month plus
$10 for the first song.
c. a tutor charges $10 per hour plus a $15
travel fee.
d. a tutor charges $15 per hour plus a $10
travel fee.

1. which scenario best describes the

equation $y = 2x + 25$?
a. a pizza place charges $25 per pizza and
$2 for delivery.
b. a bowling alley charges $2 for shoe
rentals and $25 per game.
c. a summer camp charges a $25
registration fee and $2 per day for lunch.
d. a summer camp charges a $2
registration fee and $25 per day for lunch.

1. which scenario best describes the

equation $y = 0.50x + 5$?
a. a library charges a $5 fine plus $0.50
for every day a book is late.
b. a library charges $0.50 per book and $5
for a library card.
c. a snack bar sells soda for $5 and chips
for $0.50.
d. both a and b.

Explanation:

Step1: Identify linear form $y=mx+b$

Linear equations for real-world scenarios follow $y=mx+b$, where $b$ is the fixed cost/initial value, and $m$ is the variable rate per unit $x$.

Step2: Solve Q1: Plumber cost

Fixed fee $b=75$, hourly rate $m=60$. Equation: $y=60x+75$

Step3: Solve Q2: Gym cost

Fixed sign-up fee $b=50$, monthly rate $m=30$. Equation: $y=30x+50$

Step4: Solve Q3: Bookstore cost

Fixed shipping $b=5$, per-book rate $m=15$. Equation: $y=15x+5$

Step5: Solve Q4: Taxi cost

Fixed base fee $b=2$, per-mile rate $m=3.50$. Equation: $y=3.50x+2$

Step6: Solve Q5: Savings balance

Initial amount $b=100$, weekly deposit $m=20$. Equation: $y=20x+100$

Step7: Solve Q6: Match $y=10x+15$

$m=10$ (per hour rate), $b=15$ (fixed travel fee). Matches option C.

Step8: Solve Q7: Match $y=2x+25$

$m=2$ (daily lunch rate), $b=25$ (fixed registration fee). Matches option C.

Step9: Solve Q8: Match $y=0.50x+5$

$m=0.50$ (per day late fee), $b=5$ (fixed fine). Matches option A.

Answer:

1. B. $y = 60x + 75$
2. A. $y = 30x + 50$
3. B. $y = 15x + 5$
4. B. $y = 3.50x + 2$
5. C. $y = 20x + 100$
6. C. A tutor charges $10 per hour plus a $15 travel fee.
7. C. A summer camp charges a $25 registration fee and $2 per day for lunch.
8. A. A library charges a $5 fine plus $0.50 for every day a book is late.