Linear Equations: Writing and Solving Real-Life Problems

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) as a function of miles driven (m).

• C = 50 + 0.50m

• C = 50 - 0.20m

• C = 50 + 0.20m

• C = 0.20 + 50m

If a student scores 75% on their first test and 85% on their second test, write a linear equation to represent their average score (A) after two tests based on the number of tests taken (t).

• A = (75 + 85) / 2

• A = 75 + 85

• A = (75 + 85) * t

• A = (75 + 85) / t

A gym charges a monthly membership fee of $30 and an additional $10 for each class attended. Write a linear equation for the total cost (C) based on the number of classes (c) attended in a month.

• C = 30c + 10

• C = 30 + 10c

• C = 30 + 5c

• C = 10 + 30c

If a store sells notebooks for $2 each and pens for $1 each, write a linear equation to represent the total cost (C) of buying notebooks (n) and pens (p).

• C = n + 2p

• C = 2n + p

• C = 3n + 2p

• C = 2n + 2p

A gardener charges a flat rate of $100 for a landscaping project plus $15 per hour of work. Write a linear equation to represent the total cost (C) based on hours worked (h).

• C = 100h + 15

• C = 15h - 100

• C = 100 - 15h

• C = 100 + 15h

Solve the equation 3x + 5 = 20 to find the value of x. What does this value represent in a real-world context?

• 15

• 5

• 0

• 10

A taxi company charges a base fare of $3 plus $2 for each mile driven. If a customer pays $15, how many miles did they travel? Write and solve the equation to find the answer.

• 7 miles

• 5 miles

• 6 miles

• 4 miles

A phone plan costs $40 per month plus $0.10 per text message sent. If a customer’s bill is $50, how many text messages did they send? Write and solve the equation to find the number of messages.

• 120

• 75

• 50

• 100

A school is selling tickets for a play at $10 each. If they sell 150 tickets, write a linear equation to represent the total revenue (R) from ticket sales based on the number of tickets sold (t).

• R = 100 + 10t

• R = 10t

• R = 15t

• R = 5t

If a person saves $200 initially and adds $50 each month, write a linear equation to represent their total savings (S) after m months. How much will they have saved after 6 months?

• 600

• 400

• 500

• 300