Real-Life Linear Equations: Slope and Cost Challenges

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the linear equation that represents the total cost (C) in terms of miles driven (m). What is the slope and y-intercept of this equation?

• C = 50 + 0.20m; slope = 50; y-intercept = 0

• C = 50 + 0.50m; slope = 0.50; y-intercept = 50

• C = 100 + 0.20m; slope = 0.20; y-intercept = 100

• C = 50 + 0.20m; slope = 0.20; y-intercept = 50

A gym membership costs $30 to join and $25 per month. Write a linear equation for the total cost (C) after m months. What does the slope represent in this scenario?

• C = 30 + 30m; the slope is 30.

• C = 30 + 20m; the slope is 20.

• C = 30 + 25m; the slope is 25.

• C = 25 + 30m; the slope is 30.

A delivery service charges a base fee of $5 plus $1.50 per mile. If the total cost for a delivery is $20, how many miles was the delivery?

• 5 miles

• 15 miles

• 8 miles

• 10 miles

A school is selling tickets for a play. The first 50 tickets are sold for $10 each, and after that, tickets are sold for $8 each. Write a piecewise linear equation for the total revenue (R) based on the number of tickets sold (t). What is the slope in each segment?

• R(t) = { 10t, 0 <= t <= 50; 400 + 10(t - 50), t > 50. Slope: 10 (0 <= t <= 50), 10 (t > 50)

• R(t) = { 12t, 0 <= t <= 50; 600 + 6(t - 50), t > 50. Slope: 12 (0 <= t <= 50), 6 (t > 50)

• R(t) = { 8t, 0 <= t <= 50; 400 + 5(t - 50), t > 50. Slope: 8 (0 <= t <= 50), 5 (t > 50)

• R(t) = { 10t, 0 <= t <= 50; 500 + 8(t - 50), t > 50. Slope: 10 (0 <= t <= 50), 8 (t > 50)

A bike shop sells bikes for $200 each and offers a discount of $20 for every bike purchased after the first. Write the linear equation for the total cost (C) in terms of the number of bikes (b) purchased. What does the slope indicate?

• C = 200b - 20b

• C = 180b - 20

• C = 200b + 20(b - 1)

• C = 200b - 20(b - 1)

A local bakery sells cupcakes for $3 each and offers a deal of 4 for $10. Write a linear equation for the total cost (C) based on the number of cupcakes (c) bought. How does the slope change if you buy more than 4 cupcakes?

• C = 2c for 1 <= c <= 4; C = 8 + 2(c - 4) for c > 4.

• C = 4c for c <= 4; C = 10 + 4(c - 4) for c > 4.

• C = 3c for 1 <= c <= 4; C = 10 + 3(c - 4) for c > 4.

• C = 5c for c <= 4; C = 10 + 5(c - 4) for c > 4.

A taxi company charges a flat rate of $2.50 plus $0.50 per mile. If a customer pays $12, how many miles did they travel? Write the linear equation and interpret the slope and y-intercept.

• 19 miles

• 10 miles

• 22 miles

• 15 miles

A farmer sells apples for $2 per pound and has a fixed cost of $10 for packaging. Write the linear equation for the total cost (C) in terms of pounds of apples (p). What does the y-intercept represent?

• C = 3p + 5; y-intercept represents the total cost of apples ($5).

• C = 2p + 10; y-intercept represents the fixed cost of packaging ($10).

• C = 2p + 20; y-intercept represents the variable cost of apples ($20).

• C = 4p + 10; y-intercept represents the cost of transportation ($10).

A concert venue has a seating capacity of 500. If tickets are sold for $20 each, write a linear equation for the total revenue (R) based on the number of tickets sold (t). What does the slope of this equation represent?

• R = 500t; the slope represents the total capacity of the venue.

• R = 10t; the slope represents the discount per ticket sold, which is $10.

• R = 20t + 100; the slope represents the fixed costs associated with the concert.

• R = 20t; the slope represents the revenue per ticket sold, which is $20.