Worksheet: Interpreting Linear Functions in Context

In this worksheet, we will practice interpreting linear functions in context.

Q1:

The perimeter of an isosceles triangle is 18 cm. Find the different possible lengths of its sides given they are integers.

  • A ( 8 , 8 , 2 ) , ( 7 , 7 , 4 ) , ( 5 , 5 , 8 ) , ( 4 , 4 , 1 0 )
  • B ( 8 , 8 , 2 ) , ( 7 , 7 , 4 ) , ( 5 , 5 , 8 )
  • C ( 8 , 8 , 2 ) , ( 7 , 7 , 4 )
  • D ( 7 , 7 , 4 ) , ( 5 , 5 , 8 )

Q2:

In converting temperature from Fahrenheit to Celsius, the formula 𝐢 ( 𝑓 ) = 5 9 ( 𝑓 βˆ’ 3 2 ) is used. What is the significance of 32 in the formula?

  • A The temperature 0 degrees Fahrenheit corresponds to 212 degrees Celsius.
  • BThe temperature 212 degrees Fahrenheit corresponds to 0 degrees Celsius.
  • C The temperature 0 degrees Fahrenheit corresponds to 32 degrees Celsius.
  • D The temperature 32 degrees Fahrenheit corresponds to 0 degrees Celsius.
  • E The temperature 212 degrees Fahrenheit corresponds to 32 degrees Celsius.

Q3:

A seafood restaurant serves two different kinds of fish: cod and eel. The restaurant needs no more than 75 fish each day, and it does not serve more than 35 cod and 40 eels daily. The price of a cod is 8 LE and that of an eel is 6 LE. Using π‘₯ to represent the number of cod bought each day, 𝑦 to represent the amount of eel, and 𝑝 to represent the total price, state the objective function.

  • A 8 π‘₯ + 6 𝑦 = 7 5
  • B 𝑝 < 4 0 π‘₯ + 3 5 𝑦
  • C 𝑝 = 6 π‘₯ + 8 𝑦
  • D 𝑝 = 8 π‘₯ + 6 𝑦
  • E 𝑝 = 3 5 π‘₯ + 4 0 𝑦

Q4:

Given that the perimeter of a rectangle is 22 cm, determine all the different possibilities of its length and width where both of them belong to β„€  .

  • A ( 1 , 1 0 ) , ( 2 , 9 ) , ( 3 , 8 ) , ( 4 , 7 )
  • B ( 1 , 2 1 ) , ( 2 , 2 0 ) , ( 3 , 1 9 ) , ( 4 , 1 8 ) , ( 5 , 1 7 ) , ( 6 , 1 6 ) , ( 7 , 1 5 ) , ( 8 , 1 4 ) , ( 9 , 1 3 ) , ( 1 0 , 1 2 )
  • C ( 1 , 2 1 ) , ( 2 , 2 0 ) , ( 3 , 1 9 ) , ( 4 , 1 8 )
  • D ( 1 , 1 0 ) , ( 2 , 9 ) , ( 3 , 8 ) , ( 4 , 7 ) , ( 5 , 6 )
  • E ( 1 , 2 1 ) , ( 2 , 2 0 ) , ( 3 , 1 9 ) , ( 4 , 1 8 ) , ( 5 , 1 7 )

Q5:

Find all the different possibilities of two numbers in which twice the first plus the second equals 8, given that both are even natural numbers.

  • A ( 0 , 8 ) , ( 2 , 4 )
  • B ( 0 , 8 ) , ( 1 , 6 )
  • C ( 0 , 8 ) , ( 1 , 6 ) , ( 2 , 4 ) , ( 3 , 2 ) , ( 4 , 0 )
  • D ( 0 , 8 ) , ( 2 , 4 ) , ( 4 , 0 )
  • E ( 0 , 8 ) , ( 1 , 6 ) , ( 2 , 4 )

Q6:

The cost, 𝐢 dollars, of a taxi journey includes a fixed charge plus an amount per mile. The cost of a journey of 𝑑 miles is given by the equation 𝐢 = 3 + 2 𝑑 .

How much is the fixed charge?

Q7:

In converting temperature from Fahrenheit to Celsius, the formula 𝐢 ( 𝑓 ) = 5 9 ( 𝑓 βˆ’ 3 2 ) is used. What is the significance of 5 9 in the formula?

  • A Each rise of a degree in Celsius is the same as a rise of 0 degrees Fahrenheit.
  • BEach rise of a degree in Celsius is the same as a rise of 32 degrees Fahrenheit.
  • C Each rise of a degree in Fahrenheit is the same as a rise of 5 9 degrees Celsius.
  • D Each rise of a degree in Celsius is the same as a rise of 5 9 degrees Fahrenheit.
  • E Each rise of a degree in Fahrenheit is the same as a rise of 212 degrees Fahrenheit.

Q8:

When a cyclist was moving in a straight line with a uniform velocity, the distance between the bicycle and a fixed point was registered over periods of time from the moment the cyclist took off. Find the time when the cyclist was at a distance of 140 km from the fixed point and the distance between the start point of the bicycle and the fixed point.

Distance between Bicycle and Fixed Point (kilometers) 90 110 130 150
Time Elapsed (hours) 1 2 3 4
  • Atime = 3 . 5 h , distance = 7 0 k m
  • Btime = 4 . 5 h , distance = 9 0 k m
  • Ctime = 4 . 5 h , distance = 7 0 k m
  • Dtime = 3 . 5 h , distance = 9 0 k m

Q9:

In a stationery shop, you can mix and match your own gifts. Each gift comprises of a pencil case, and a mixture of pens, coloring pencils, and erasers. The pencil case costs $3 and Michael spends $15 on his gift.

Let 𝑝 be the number of pens Michael includes in his gift, 𝑐 the number of coloring pencils, and 𝑒 the number of erasers.

Michael’s gift satisfies the following equations: 𝑝 + 𝑐 + 𝑒 = 1 0 , 2 . 5 𝑝 + 𝑐 + 0 . 5 𝑒 + 3 = 1 5 .

How many items did Michael put in the pencil case?

What is the cost of an eraser?

What is the cost of a coloring pencil?

Q10:

The cost to borrow 𝑛 books from a library is given for one year by 𝐢 = 1 0 + 1 . 5 𝑛 . What do the parameters 10 and 1.5 represent?

  • A$10 is the fixed cost per year, and $1.50 is the cost per borrowed book.
  • B$10 is the fixed cost per year, and $1.50 is the cost per 100 borrowed books.
  • C$10 is the fixed cost per year, and $1.50 is the total cost for n books.
  • D$10 is the variable cost per year, and $1.50 is the cost per borrowed book.
  • E$10 is the cost per borrowed book, and $1.50 is the fixed cost per year.

Q11:

What is the 𝑦 -intercept of the linear function 𝑦 = 3 π‘₯ + 2 ?

Q12:

Liam is trying to decide which summer camp to attend. The relationship between the number of days and the cost of attending is linear for each camp. Write the corresponding linear functions that describe each summer camp’s total cost.

Camp A $50 per day $20 registration fee
Camp B 2 days cost $90 7 days cost $280
  • Acamp A: 𝑦 = 5 0 π‘₯ βˆ’ 2 0 , camp B: 𝑦 = 3 8 π‘₯ + 1 4
  • Bcamp A: 𝑦 = 5 0 π‘₯ + 2 0 , camp B: 𝑦 = 3 8 π‘₯ + 1 4
  • Ccamp A: 𝑦 = 2 0 π‘₯ + 5 0 , camp B: 𝑦 = 1 4 π‘₯ + 3 8
  • Dcamp A: 𝑦 = 5 0 π‘₯ + 2 0 , camp B: 𝑦 = π‘₯ 3 8 + 1 4
  • Ecamp A: 𝑦 = π‘₯ 5 0 + 2 0 , camp B: 𝑦 = 3 8 π‘₯ + 1 4

Q13:

A rise of 1 degree Fahrenheit is the same as 5 9 degree kelvin. Since absolute zero, 0 K, is the same as βˆ’ 4 5 9 . 6 7 ∘ F , what is the formula for converting Fahrenheit to Kelvin?

  • A π‘˜ = 5 9 𝑓 βˆ’ 4 5 9 . 6 7
  • B π‘˜ = 5 9 ( 𝑓 + 4 5 9 . 6 7 )
  • C π‘˜ = 9 5 ( 𝑓 + 4 5 9 . 6 7 )
  • D π‘˜ = 𝑓 + 4 5 9 . 6 7
  • E π‘˜ = 9 5 𝑓 βˆ’ 4 5 9 . 6 7

Q14:

A cable television offers its service at $45 per month and a one-time setup fee of $19.95. Express the total amount paid 𝑃 ( 𝑛 ) after 𝑛 β‰₯ 0 months by an explicit formula on the set of whole numbers.

  • A 𝑃 ( 𝑛 + 1 ) = 1 9 . 9 5 + 4 5 𝑛 , 𝑃 ( 0 ) = 4 5
  • B 𝑃 ( 𝑛 ) = 1 9 . 9 5 𝑛 + 4 5
  • C 𝑃 ( 𝑛 ) = 1 9 . 9 5 + 4 5 𝑛
  • D 𝑃 ( 𝑛 + 1 ) = 𝑃 ( 𝑛 ) + 4 5
  • E 𝑃 ( 𝑛 ) = 1 9 . 9 5 ( 𝑛 βˆ’ 1 ) + 4 5 , 𝑃 ( 0 ) = 1 8 . 6 0

Q15:

A school organised a trip where there is a fixed cost of 59 pounds and the rest of the cost is dependent on the number of students attending. The total cost for a trip with 41 students is 387 pounds. Find the linear function representing the total cost 𝑓 ( 𝑛 ) , based on the number of students 𝑛 .

  • A 𝑓 ( 𝑛 ) = 8 𝑛 + 5 9
  • B 𝑓 ( 𝑛 ) = 9 𝑛 + 5 9
  • C 𝑓 ( 𝑛 ) = 𝑛 + 5 9
  • D 𝑓 ( 𝑛 ) = 8 𝑛 + 3 8 7
  • E 𝑓 ( 𝑛 ) = 9 𝑛 + 3 8 7

Q16:

A boy was reading a book and found out that after reading for 4 hours he still had 420 pages left to read. After reading for 6 hours he still had 314 pages left to read. If the relation between the number of pages read and the time it takes to read is linear, how many pages does the book have?

Q17:

David filled up his car with fuel. After driving for 120 km, David had 1 4 of a tank of fuel left. Assuming the relationship between fuel and distance traveled is linear, calculate the total distance David can drive.

  • A 600 km
  • B 160 km
  • C 40 km
  • D 360 km
  • E 480 km

Q18:

An online eBook store charges $30 a year for a membership and $2 for each book downloaded. Write a function rule to represent the total cost, letting 𝑠 represent the number of books and 𝑑 the total cost. Then, use the function rule to determine the total cost if you download 52 books in a year.

  • A 𝑑 = 2 𝑠 βˆ’ 3 0 , $74
  • B 𝑑 = 2 𝑠 + 3 0 , $134
  • C 𝑑 = 3 0 𝑠 + 2 , $1,562
  • D 𝑑 = 3 0 𝑠 βˆ’ 2 , $1,558
  • E 𝑑 = 𝑠 βˆ’ 2 8 , $24

Q19:

The cost of moving a package is 207 LE per box. What is the function that represents the cost of moving multiple boxes?

  • A 𝑓 ( π‘₯ ) = π‘₯ 2 0 7
  • B 𝑓 ( π‘₯ ) = 2 0 7 π‘₯
  • C 𝑓 ( π‘₯ ) = 2 0 7 π‘₯
  • D 𝑓 ( π‘₯ ) = π‘₯ + 2 0 7

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