Linear Equations in Context

At the beginning of October, Monique changed banks and decided to leave the remaining $3900 in her old checking account to pay for rent. After six months, her balance was finally zero. If the balance, B, in Monique’s account is a function of time, t, write an equation for the situation.

• B = 3900 – 650t

• B = 3900 + 650t

• B = 3900t – 650t

• B = 3900t + 650t

On a recent scuba diving trip, Kate and Kara reached a depth of 130 feet. Six-and- a-half minutes later after ascending at a constant rate, they reached the surface. Write an equation to represent their distance, D, as a function of time, t.

• D = 130 – 20t

• D = 130 + 20t

• D = 20 – 130t

• D = 20 + 130t

Cedric and Josh both ordered the same size pizzas at Marco’s Pizzeria; however, they ordered different toppings. Marco’s charges an additional fee for toppings, but all toppings cost the same. Cedric got pepperoni, banana peppers, and black olives on his pizza for a cost of $15.74. Josh ordered mushrooms and eggplant on his pizza and paid $14.49. Using this information, write an equation for the cost of a pizza, C, as a function of the number of toppings, t ordered.

• C = 11.99 + 1.25t

• C = 11.99 - 1.25t

• C = 11.99t + 1.25

• C = 11.99t - 1.25

Margaret purchased a new bar of soap. Three days after she originally used the soap, she was curious how much soap per day she was using. She decided to weigh her soap and found that the bar was 103 grams. Four days later she re-measured the same bar of soap and recorded a weight of 80 grams. Assuming that Margaret uses the same amount of soap daily (and that she used the soap daily), write an equation that shows the amount of soap remaining after d days of use.

• S = 120.25 – 5.75d

• S = 120.25 + 5.75d

• S = 120.25d – 5.75

• S = 120.25d + 5.75

Kylie is ordering a taxi from an online taxi service. She has to pay a flat charge just to order the taxi, and then has to pay per mile, depending on how far she travels. She wrote an equation to represent her total cost, y=3.5+2.3x, where y represents the total cost in dollars and cents, and x represents the number of miles she travels. What could the number 3.5 represent in the equation?

• How much the taxi costs per mile

• Total charge for one mile

• The flat charge to order the taxi

• How far Kylie can ride for $1

Starting at noon, Emily observed the amount of snow on her lawn during a blizzard. She wrote an equation to represent s, how many inches of snow were on the lawn: s=0.024x+7, where x represents the number of minutes past noon. What could the number 0.024 represent in the equation?

• The amount of snow on the lawn at 12:01 pm

• The amount of snow on the lawn at noon

• How much more snow is added to the lawn every minute

• The total amount of snow

Jocelyn is going to the amusement park, where she has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money Jocelyn will spend is given by the equation y=3.5x+28, where y represents the total amount of money, in dollars and cents, and x represents the number of rides Jocelyn goes on. What could the number 28 represent in the equation?

• The total amount Jocelyn will spend if she goes on 1 ride

• The change in total amount of money for each additional ride she goes on

• The total amount Jocelyn will spend if she goes on 100 rides

• The cost to get into the amusement park

Anthony's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=57+6.3x, where y represents the expected quiz score and x represents hours spent on homework that week. What is the meaning of the x-value when y=99?

• A student's expected quiz score if they spend 1 hour on their homework

• A student's expected quiz score if they spend 99 hours on their homework

• How many hours a student spends studying all year

• The number of hours a student should spend on their homework to expect a score of 99 on the quiz

Nathaniel is taking a multiple choice test. His grade is given by the equation y=105−3x, where y represents his final score and x represents the number of questions he got wrong. What is the meaning of the y-value when x=1?

• The score he would get if he only missed one question

• The number of problems on the test

• His score with 0 problems wrong

• The points he loses for every wrong question

At the beginning of spring, Lauren planted a small sunflower in her backyard. The sunflower's height in inches, h, after w weeks, is given by the equation h=9+3w. What could the number 9 represent in the equation?

• The sunflower's height when it was planted

• The sunflower's final height

• The rate of change in the sunflower's height

• The sunflower's height after one week