COMPARING UNIT RATE WORD PROBLEMS WORKSHEET

Examine each set of functions and determine which has the greater rate of change, if either. Explain your reasoning.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Alicia, Cherie, and John had been studying rates of change and were discussing the best way to determine which linear function has the greater rate of change.

Solution

Examine each set of functions and determine which has the greater rate of change, if either. Explain your reasoning.

Problem 5 :

Match each description of the situation with its corresponding graph. Explain your reasoning.

a. A person gives $20 per week to a friend to repay a $200 loan.

b. An employee receives $12.50 per hour plus $2 for each unit produced per hour.

c. A sales representative receives $30 per day for food plus $0.565 for each mile driven.

d. A computer that was purchased for $750 depreciates $100 per year.

Solution

Problem 6 :

The function C(x) = 17.5x − 10 represents the cost (in dollars) of buying x tickets to the orchestra with a $10 coupon.

a. How much does it cost to buy five tickets?

b. How many tickets can you buy with $130?

Solution

Problem 7 :

Account A earns simple interest. Account B earns compound interest. The table shows the balances for 5 years. Graph the data and compare the graphs.

Solution

Examine each set of functions and determine which has the greater rate of change, if either. Explain your reasoning.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Equation A  : 5x + 6y = 60

Equation B  : y = (-1/4)x  - 2

Solution

Problem 4 :

An ice cream shop is choosing a milk delivery service. The Spotted Cow charges $2.80 per gallon, plus a $2 delivery fee. Dairy Farms charges $2.10 per gallon, plus a $10 delivery fee.

Solution

Problem 5 :

The Metropolis Zoo recently celebrated the birth of two new baby pandas.

Mochi the panda cub has been measured and weighted each week since she was born.

Mochi’s brother is Kappa. His weight has been charted on the graph below.

1. Which panda was heavier when born?

2. How fast is Mochi growing (rate of change)? How fast is Kappa growing (rate of change)?

3. Which panda will weigh more at 5 weeks?

Solution

Problem 1 :

Alan and Margot each drive from City A to City B, a distance of 𝟏𝟒𝟕 miles. They take the same route and drive at constant speeds. Alan begins driving at 1:40 p.m. and arrives at City B at 4:15 p.m.

Margot’s trip from City A to City B can be described with the equation 𝒚 = 𝟔𝟒x, where y is the distance traveled in miles and 𝒙 is the time in minutes spent traveling.

Who gets from City A to City B faster?           Solution

Problem 2 :

You have recently begun researching phone billing plans. Phone Company A charges a flat rate of $𝟕𝟓 a month. A flat rate means that your bill will be $𝟕𝟓 each month with no additional costs.

The billing plan for Phone Company B is a linear function of the number of texts that you send that month. That is, the total cost of the bill changes each month depending on how many texts you send.

The table below represents some inputs and the corresponding outputs that the function assigns.

(i)  At what number of texts would the bill from each phone plan be the same?

(ii)  At what number of texts is Phone Company A the better choice?

(iii)  At what number of texts is Phone Company B the better choice?                      Solution

Problem 3 :

Two people, Adam and Bianca, are competing to see who can save the most money in one month. Use the table and the graph below to determine who will save the most money at the end of the month. State how much money each person had at the start of the competition. (Assume each is following a linear function in his or her saving habit.)

Solution

Problem 4 :

Two contestants on Biggest Loser are Valerie and Oscar. Their weight loss is shown below.

Valerie’s weight loss is shown by this function, where 𝑊 is her weight in pounds and 𝑡 is time in weeks.

𝑊 = 235 − 2.5𝑡

Oscar’s weight loss is tracked in the table

1. Who weighed more at the beginning of the show?

2. How much weight is Valerie losing per week (rate of change)?

3. How much weight is Oscar losing per week (rate of change)?

4. Who is losing weight faster?

Solution