Writing Equations and Inequalities

Tricia and Melanie are both saving money for their summer vacations. They both began saving at the same time. Tricia started with $10.25 and adds $5.15 to her savings every month. Melanie did not have a starting amount but adds $10.25 to her savings every month. Which equation could be used to determine how many months, m, it will take before Tricia and Melanie both have saved the same amount of money?

• 5.15m + 10.25 = 10.25m

• 10.25m + 5.15 = 10.25m

• 10.25m + 10.25 = 5.15m

• 10.25m – 5.15 = 10.25m

Jack and Tim are racing remote-controlled cars. Jack’s car travels 3.5 feet per second, while Tim’s car travels 5.25 feet per second. Because Jack’s car is slower, Tim gave Jack a 10-foot head start. Which inequality could be used to determine after how many seconds, s, Tim’s car will be ahead of Jack’s car?

• 3.5s > 5.25s + 10

• 3.5s + 10 > 5.25s

• 5.25s > 3.5s + 10

• 3.5s – 10 < 5.25s

Laura has two large cylindrical barrels of solution in her chemical laboratory. The first barrel contains 900 liters of solution, and the second barrel contains 100 liters of solution.

Laura drains the first barrel at a rate of 36 liters per minute. Laura fills the second barrel at a rate of 44 liters per minute.

Which inequality represents the minutes, m, when the

second barrel contains a greater or equal amount

of solution than the first barrel?

• –36m + 100 < 44m + 900

• 900 + 36m ≤ 100 – 44m

• –36m + 900 ≤ 44m + 100

• 100 + 36m < 900 – 44m

Jacelyn’s company required an initial investment of $2,125 for starting costs and sells construction toys for $49.99 each. Richie’s company required no initial investment and sells construction toys online for $39.95 each. Which equation can be used to find t, the number of construction toys that must be bought so that the profit for Jacelyn’s company and Richie’s company is the same?

• 49.99t + 2125 = 39.95t

• 39.95t – 2125 = 49.99t

• –2075.01t = 39.95t

• 49.99t – 2125 = 39.95t

Ten packs of tickets for rides at an amusement park sell for $125.00. One family has already used two of their tickets. They now have 9.6 packs left. Which equation can be used to find t, the number of tickets in each package, and the value of t that makes the equation true?

• 9.6t – 2 = 10t

  t = 0.8

• 9.6t + 2 = 10t

  t = 5

• 9.6t = 10t + 2

  t = –5

• 9.6t = 10t – 2

  t = –0.8

Jocy has two tanks for holding water on her property. Both tanks are 50 inches tall. Tank A is empty and Jocy is filling the tank. For each minute Jocy is filling the tank, the height of the water in Tank A increases by 3.7 inches. Tank B is full and Jocy is draining the tank. For each minute Jocy is draining the tank, the height of the water in Tank B decreases by 1.9 inches. Approximately how many minutes will pass so the height of the water in Tank A and Tank B is the same?

• 112 minutes

• 28 minutes

• 56 minutes

• 9 minutes

Which of the following situations can be modeled by the inequality 35 + 0.12x < 12.99 + 0.33x?

• Package Delivery Service A charges $35 per package plus 33 cents per mile. Package Delivery Service B charges $12.99 per package plus 12 cents per mile. For what distance is Package Delivery A more expensive?

• Window Washer A charges $35 per building plus 33 cents per window. Window Washer B charges $12.99 per building plus 12 cents per window. For What number of windows is Window Washer A more expensive?

• Cell phone plan A changes $35 per month plus 12 cents per minute. Cell phone plan B charges $12.99 per month plus 33 cents per minute. For what number of minutes is Plan A less expensive?

• Car Rental Company A charges $35 plus 12 cents per mile. Car Rental Company B charges $12.99 plus 33 cents per mile. For what number of miles is Company A more expensive?

Which situation can be represented by this equation? 68+20x = 780-14x

• Sarah has $68 in her savings account and deposits $20 in it every week. John has $780 in his savings account and withdraws $14 from it every week.

  What is x, the number of weeks that will need to pass before they have the same balance in their accounts?

• April has 20 pennies in a jar and adds 68 more pennies per week. Ben has 14 pennies in a jar and adds 780 more at one time. After how many weeks will April have the same amount of pennies as Ben?

• Callie is filling up a pool that currently has 68 gallons of water in it. She adds 14 gallons per minutes to the pool. Erik's pool is already full and has 780 gallons of water in it, but the pool is leaking at a rate of 20 gallons per minute. After how many minutes will Callie and Erik's pools have the same amount of water?

• Gail has 88 narwhals and Kody has 766 narwahls. Gail gains 20 narwhals to her narwhal herd each week and Kody loses 14 narwhals from his narwhal herd each week. After how many weeks do they have the same amount of narwhals?

Zoe needs to rent a car. Kara's Kar Kompany charges $22 per day and a $100 cleaning fee. Callie's Car Company charges $26 per day and has a $40 cleaning fee. After how many days would the rental cost be the same for both car rental companies?

• 8 Days

• 13 Days

• 15 Days

• 18 Days

A student writes the following word problem for the equation 250 + x = 146 + 5x.

Kevin saves $1 per day. He opens his account with $250. Mandy saves $5 per day. She opens her account with $146. After how many days will they have the same amount?

Is the student’s word problem appropriate for the equation?

• Yes, both accounts will have x dollars.

• Yes, the amount in each account will be equal after x days.

• No, the constants on each side been switched

• No, the coefficients on x on each side of the equation have been switched.