Creating and Solving Equations and Inequalities Flashcards

A plumber charges a flat fee of $50 for a service call, plus $75 per hour of work. If a customer's total bill was $425, which equation could be used to find the number of hours, h, the plumber worked?

Answer: 75h + 50 = 425

The total cost is the sum of the flat fee ($50) and the variable cost, which is the hourly rate ($75) multiplied by the number of hours (h). Therefore, the equation is 75h + 50 = 425.

Maria is saving for a new laptop that costs $1,200. She has already saved $450. She earns $15 per hour at her part-time job. What is the minimum number of hours she must work to afford the laptop?

Answer: 50 hours

Let h be the hours Maria works. Her earnings are 15h. Her total savings will be her current savings plus her earnings: 450 + 15h. She needs this amount to be at least $1,200. The inequality is 450 + 15h ≥ 1200. Solving for h gives h ≥ 50.

A school sold 300 tickets for a play. Student tickets cost $5 each and adult tickets cost $8 each. If the school collected a total of $1,950, how many adult tickets were sold?

Answer: 150

Let 's' be the number of student tickets and 'a' be the number of adult tickets. We have two equations: s + a = 300 and 5s + 8a = 1950. Solving the first for s (s = 300 - a) and substituting into the second gives 5(300 - a) + 8a = 1950, which simplifies to 1500 - 5a + 8a = 1950, then 3a = 450, so a = 150.

Gym A charges a $100 membership fee plus $20 per month. Gym B charges a $50 membership fee plus $30 per month. After how many months will the total cost of both gyms be the same?

Answer: 5 months

Set the cost expressions for both gyms equal to each other. Let 'm' be the number of months. The equation is 100 + 20m = 50 + 30m. Solving for m gives 50 = 10m, so m = 5.

Kevin has a $50 gift card to an online music store. Each song costs $1.29. He must have at least $10 remaining on the card to keep the account active. What is the maximum number of songs he can buy?

Answer: 31

Let 's' be the number of songs. The cost is 1.29s. The remaining balance is 50 - 1.29s. This amount must be greater than or equal to $10. The inequality is 50 - 1.29s ≥ 10. Solving gives 40 ≥ 1.29s, which means s ≤ 31.007. Since he can't buy a fraction of a song, the maximum is 31.

A car rental company charges $40 per day plus $0.25 per mile driven. If a person rents a car for 3 days and their total bill is $270, how many miles did they drive?

Answer: 600 miles

Let 'm' be the number of miles. The cost for the days is 3 * $40 = $120. The cost for the miles is 0.25m. The total cost equation is 120 + 0.25m = 270. Subtracting 120 gives 0.25m = 150. Dividing by 0.25 gives m = 600.

A group of friends wants to go to an amusement park. There is a one-time parking fee of $25, and each ticket costs $60. If they have a total budget of $500, what is the maximum number of people that can go?

Answer: 7

Let 'p' be the number of people. The total cost is the price of the tickets (60p) plus the parking fee (25). This total cost must be less than or equal to their budget. The inequality is 60p + 25 ≤ 500. Solving for p: 60p ≤ 475, so p ≤ 7.91. Since you can't have a fraction of a person, the maximum number is 7.