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Worksheet: Introduction to Equations

Q1:

Michael wants to buy a video game that costs $70. If Michael has $10, which of the following equations represents the amount of money he needs to buy the video game?

  • A 1 0 βˆ’ 𝑑 = 7 0
  • B 𝑑 βˆ’ 1 0 = 7 0
  • C 𝑑 βˆ’ 1 0 = 8 0
  • D 𝑑 + 1 0 = 7 0
  • E 𝑑 + 1 0 = 8 0

Q2:

If a football player can run 21 yards in 3.9 seconds, determine which of the following equations could be used to find the number of yards 𝑦 the player can run in a second.

  • A 3 . 9 + 𝑦 = 2 1
  • B 2 1 𝑦 = 3 . 9
  • C 3 . 9 βˆ’ 𝑦 = 2 1
  • D 3 . 9 𝑦 = 2 1
  • E 2 1 βˆ’ 𝑦 = 3 . 9

Q3:

Given that it costs $12 for each hour of snorkeling and that the cost of the equipment is $11, determine the equation that represents the cost in dollars, 𝑐 , for snorkeling for β„Ž hours.

  • A 𝑐 = 1 2 ( β„Ž + 1 1 )
  • B 𝑐 = 1 1 β„Ž + 1 2
  • C 𝑐 = 1 1 ( β„Ž + 1 2 )
  • D 𝑐 = 1 2 β„Ž + 1 1
  • E 𝑐 = β„Ž + 2 3

Q4:

The width of a bookshelf is 4 feet shorter than its height. Given that its width is 1.1 feet, write an equation that represents the height of the bookshelf.

  • A 4 β„Ž = 1 . 1
  • B β„Ž + 4 = 1 . 1
  • C β„Ž 4 = 1 . 1
  • D β„Ž βˆ’ 4 = 1 . 1
  • E β„Ž + 1 . 1 = 4

Q5:

In 2003, the population of a town was 4 5 0 0 0 , and the population has been growing linearly by 1 7 0 0 people each year. Write an equation for the population, 𝑃 ( 𝑑 ) , where 𝑑 is the number of years after 2003.

  • A 𝑃 ( 𝑑 ) = 1 7 0 0 + 4 5 0 0 0 𝑑
  • B 𝑃 ( 𝑑 ) = 4 5 0 0 0 βˆ’ 1 7 0 0 𝑑
  • C 𝑃 ( 𝑑 ) = 4 6 7 0 0 + 1 7 0 0 𝑑
  • D 𝑃 ( 𝑑 ) = 4 5 0 0 0 + 1 7 0 0 𝑑
  • E 𝑃 ( 𝑑 ) = 4 6 7 0 0 βˆ’ 1 7 0 0 𝑑

Q6:

Daniel drove 231 miles in 3.8 hours. Which of the following equations can you use to find the rate π‘Ÿ at which he was traveling?

  • A 2 3 1 π‘Ÿ = 3 . 8
  • B 2 3 1 Γ— 3 . 8 = π‘Ÿ
  • C π‘Ÿ 2 3 1 = 3 8
  • D 2 3 1 = 3 . 8 π‘Ÿ

Q7:

Express the following sentence in algebraic form: The price increased by $6 is $35.

  • A 𝑛 βˆ’ 6 = 3 5
  • B 𝑛 βˆ’ 6 = 4 1
  • C 𝑛 + 3 5 = 6
  • D 𝑛 + 6 = 3 5
  • E 𝑛 + 6 = 4 1

Q8:

An animal shelter relies on donations to look after the cats and dogs. It costs $ π‘₯ to care for a cat and $ 𝑦 to care for a dog.

Let the number of cats at the shelter be 𝑐 and the number of dogs be 𝑑 .

Write an equation for the total daily cost in dollars, 𝐢 , of looking after the cats and dogs.

  • A 𝐢 = π‘₯ + 𝑦 + 𝑐 + 𝑑
  • B 𝐢 = π‘₯ 𝑦 + 𝑐 𝑑
  • C 𝐢 = π‘₯ 𝑦 𝑐 𝑑
  • D 𝐢 = π‘₯ 𝑐 + 𝑦 𝑑
  • E 𝐢 = ( π‘₯ + 𝑦 ) ( 𝑐 + 𝑑 )

Q9:

Which of the following means β€œThe difference between π‘₯ and five times 𝑦 is 19”?

  • A 5 π‘₯ βˆ’ 𝑦 = 1 9
  • B π‘₯ + 5 𝑦 = 1 9
  • C π‘₯ βˆ’ 1 9 𝑦 = 5
  • D π‘₯ βˆ’ 5 𝑦 = 1 9
  • E 1 9 π‘₯ βˆ’ 𝑦 = 5

Q10:

Amelia says that there is no number π‘₯ whose additive inverse is the same as its multiplicative inverse. Write down the equation that such a value of π‘₯ would have to satisfy.

(Hint: we may suppose that π‘₯ β‰  0 . Why?)

  • A π‘₯ = 0 2
  • B π‘₯ = 1 2
  • C π‘₯ = βˆ’ 1
  • D π‘₯ = βˆ’ 1 2

Q11:

The sum of two numbers, π‘₯ and 𝑦 , is 17. What is the mathematical relation between π‘₯ and 𝑦 ?

  • A π‘₯ = 3 4 βˆ’ 𝑦
  • B π‘₯ = 8 βˆ’ 𝑦
  • C π‘₯ = 2 π‘₯ βˆ’ 𝑦
  • D π‘₯ = 1 7 βˆ’ 𝑦

Q12:

Suppose a vehicle is traveling at π‘Ÿ miles per hour. Which equation describes the total distance 𝐷 traveled by the vehicle, in miles, after a period of 9 hours?

  • A 𝐷 = 9 π‘Ÿ
  • B 𝐷 = π‘Ÿ 9
  • C 𝐷 = 9 + π‘Ÿ
  • D 𝐷 = 9 π‘Ÿ
  • E 𝐷 = π‘Ÿ βˆ’ 9

Q13:

Express the following phrase as an algebraic equation: The product of 𝑧 and βˆ’ 4 is 48.

  • A 𝑧 4 8 = βˆ’ 4
  • B 4 8 𝑧 = βˆ’ 4
  • C 𝑧 4 = 4 8
  • D βˆ’ 4 𝑧 = 4 8
  • E 𝑧 + 4 8 = βˆ’ 4

Q14:

Express the following phrase as an algebraic equation: The product of 𝑧 and 4 is 32.

  • A 𝑧 3 2 = 4
  • B 3 2 𝑧 = 4
  • C 𝑧 4 = 3 2
  • D 4 𝑧 = 3 2
  • E 𝑧 + 3 2 = 4

Q15:

A car rental company charges $ 1 5 per hour. Write an equation to represent this scenario using β„Ž for the number of hours and 𝑑 for the total cost.

  • A 𝑑 = 1 5 + β„Ž
  • B β„Ž = 1 5 𝑑
  • C 𝑑 = 1 5 βˆ’ β„Ž
  • D 𝑑 = 1 5 β„Ž
  • E β„Ž = 𝑑 + 1 5

Q16:

William spent a total of 93 minutes this week working out. Which of the following equations represents the number of m i n u t e s William spent doing sit-ups?

Exercise Push-ups Sit-ups
Time (min) 79 ?
  • A 7 9 βˆ’ π‘š = 9 3
  • B π‘š βˆ’ 7 9 = 9 3
  • C π‘š = 9 3 + 7 9
  • D π‘š + 7 9 = 9 3
  • E π‘š + 9 3 = 7 9

Q17:

The table shows the results of a survey which asked a group of students to pick their favorite music genre. If 288 students were surveyed, which equation can be used to find the number of students who chose Jazz?

Genre Pop Jazz Rap
Fraction of Students 1 6 1 3 1 2
  • A 1 6 𝑠 = 2 8 8
  • B 1 3 𝑠 = 2 8 8
  • C 𝑠 = 1 6 Γ— 2 8 8
  • D 𝑠 = 1 3 Γ— 2 8 8
  • E 𝑠 + 1 2 = 2 8 8

Q18:

Hannah bought 3 magazines for $28, $11 and $14 with a tax of $2. If she received $5 back as change, write a subtraction equation to determine how much money Hannah gave the cashier, and then solve it.

  • A π‘₯ βˆ’ 4 8 = 2 , π‘₯ = 5 0
  • B π‘₯ βˆ’ 5 8 = 2 , π‘₯ = 6 0
  • C π‘₯ βˆ’ 5 = 5 5 , π‘₯ = 5 0
  • D π‘₯ βˆ’ 5 5 = 5 , π‘₯ = 6 0
  • E π‘₯ βˆ’ 2 = 5 8 , π‘₯ = 5 6

Q19:

Michael can drive 65 miles in 5 hours. Write an equation to find the number of miles, π‘š , Michael can drive in β„Ž hours.

  • A π‘š = 6 5 β„Ž
  • B 1 3 π‘š = β„Ž
  • C 6 5 π‘š = β„Ž
  • D π‘š = 1 3 β„Ž
  • E 6 5 π‘š = 1 3 β„Ž

Q20:

A store is having a sale. The table shows the regular price π‘Ÿ and the sale price 𝑠 of various items. Which of the following can be used to calculate the sale price?

Item Regular Price ( π‘Ÿ ) Sale Price ( 𝑠 )
A $17.00 $9.35
B $19.00 $10.45
C $13.00 $7.15
D $20.00 $11.00
  • A 𝑠 = π‘Ÿ βˆ’ 0 . 5 5
  • B 𝑠 = π‘Ÿ Γ— 0 . 4 5
  • C 𝑠 = π‘Ÿ βˆ’ 0 . 4 5
  • D 𝑠 = π‘Ÿ Γ— 0 . 5 5
  • E 𝑠 = π‘Ÿ + 0 . 5 5

Q21:

A group of 8 friends want to buy a new couch for $492 with a tax of $44. Write a multiplication equation to determine the amount of money each person should pay if the amount is divided equally, and then solve it.

  • A 8 π‘₯ = 4 4 8 , π‘₯ = 5 6
  • B 4 4 π‘₯ = 4 9 2 , π‘₯ = 5 5
  • C 4 4 π‘₯ = 5 0 0 , π‘₯ = 1 9
  • D 8 π‘₯ = 5 3 6 , π‘₯ = 6 7
  • E 4 4 π‘₯ = 4 8 4 , π‘₯ = 7 8

Q22:

If π‘₯ is 14 more than three times 𝑦 , which of the following must be true?

  • A π‘₯ βˆ’ 1 4 𝑦 = 3
  • B π‘₯ βˆ’ 2 𝑦 = 1 4
  • C 1 4 π‘₯ = 3 𝑦
  • D π‘₯ βˆ’ 3 𝑦 = 1 4
  • E 3 π‘₯ = 1 4 𝑦