How to Write an Equation

Jody has two salary options. She can earn a salary of $500 per week plus 2% of the weekly sales or a salary of $200 per week plus 5% of the weekly sales. Which equation shows the amount in sales in order for both options to be the same?

• 200 + 2x = 500 + 5x
•  500 + 0.02x = 200 + 0.05x

Mr. Smith needs to hire a plumber to do repairs at his house. The table shows the amounts Company A and Company B charges for a service call and their hourly rate. Which inequality represents the number of hours that would make Company B less expensive than Company A?
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• 75 + 20x > 55 + 44x
• 75 + 44x > 55 + 20x
• 75 + 20x < 55 + 44x
• 75 + 44x < 55 + 20x

Which situation can be represented by the equation
100 – 2x = 140 – 6x?

• Tank A has 100 gallons of water and gains 2 gallons per hour. Tank B has 140 gallons and gains 6 gallons per hour. When will the tanks have the same amount of water?
• Tank A has 100 gallons of water and loses 2 gallons per hour. Tank B has 140 gallons and loses 6 gallons per hour. When will the tanks have the same amount of water?
• Tank A has 100 gallons of water and gains 2 gallons per hour. Tank B has 140 gallons and gains 6 gallons per hour. When will Tank A have more water than Tank B?
• Tank A has 100 gallons of water and loses 2 gallons per hour. Tank B has 140 gallons and loses 6 gallons per hour. When will Tank A have more water than Tank B?

1.  In Brownsville, Texas, it is 88 degrees Fahrenheit.  The temperature is expected to drop 1.5 degrees each hour.  In Mesquite, Texas it is 94 degrees Fahrenheit, and the temperature is expected to drop 2 degrees each hour.  In how many hours will the temperature in Mesquite be greater than the temperature in Brownsville?

• 88 - 2x > 94 - 1.5x      
• 1.5x - 88 < 2x - 94
• 88 - 1.5x < 94 - 2x
• 88 - 1.5x > 94 - 2x

Natalie is going mountain biking. She can buy a bike for $250 or she can rent a bike for $30 an hour. In both cases, she must also rent a helmet for $5 an hour. Which inequality shows the number of hours Natalie must bike for the cost of buying a bike to be less than renting a bike?

• 250 + 5x > 30x
• 250 + 5x > 35x
• 250 + 5x < 30x
• 250 + 5x < 35x

Which situation is represented by inequality 25x + 500 ≥ 50x + 250?

• Corey earns $25 for each insurance policy he sells plus $500 each week. Maria earns $50 for each policy she sells plus $250 each week. How many policies will each employee need to sell so that Maria earns the same or more than Corey?
• Corey earns $50 for each insurance policy he sells plus $500 each week. Maria earns $25 for each policy she sells plus $250 each week. How many policies will each employee need to sell so that Maria earns the same or more than Corey?
• Corey earns $25 for each insurance policy he sells plus $500 each week. Maria earns $50 for each policy she sells plus $250 each week. How many policies will each employee need to sell so that Maria earns the same or less than Corey?

Rent Games Now charges a $7.95 per game for rentals, and you can keep the game as long as you like. Last year, Jennifer bought a used PS3 for $149.99. After renting several games, she spent a total of $436.19 to play games. How many games did she rent? Write the linear equation and solve for the number of games.

• 7.95x + 149.99x = 436.19; 2.76 games
• 149.99 - 7.95x = 7.95 ; 18 games
• 7.95x + 149.99 = 436.19; 36 games
• 7.95x + 149.95 = 15; 28 games

Merced Mega school sells wrapping paper to raise money for student activities. The school keeps half of all the sales, minus $300 for prizes for top sellers. How much wrapping paper must be sold for the school to earn $5000. Write the linear equation and solve.

• 5000 = 1/2x - 300      $10,600
• 5000 = 2x - 300   $2,650
• 5000 = 1/2x + 300   $2,650
• 5000 = 2x + 300      $10,600

The total amount of allowance that Matt receives includes a base amount, plus an amount that depends on the number of chores he completes. He received $16 in allowance the week he did 12 chores and he received $14 in allowance the week he did 8 chores. What equation represents this situation?

• y = 0.5x + 10
• y = 1/2x + 10
• y = x/2 + 10
• all of the above

A camp charges families a fee of $625 per month for one child and a certain amount more per month for each additional child. Use the graph to write an equation in slope-intercept form to represent the amount a family with x additional children would pay.

• y = 625x + 225
• y = 225x 
• y = 225x + 625
• y =  625