Worksheet: Introduction to Equations

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In this worksheet, we will practice reading and writing algebraic equations and figuring out what value of the variable will make a true equation.

Q1:

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

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

Q2:

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

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

Q4:

William spent a total of 93 minutes this week working out. Which of the following equations represents the number of minutesWilliam spent doing sit-ups?

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

Q5:

Which of the following could be described by 64+π‘₯=81?

  • A π‘₯ passengers were on a bus. When 81 passengers got off the bus, there were 64 passengers left.
  • B64 passengers were on a bus. When π‘₯ passengers got on the bus, the total number of passengers was 81.
  • C64 passengers were on a bus. When 81 passengers joined them, the total was π‘₯.
  • D π‘₯ passengers were on a bus. When 64 passengers got off the bus, there were 81 passengers left.

Q6:

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

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

Q7:

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

Q8:

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

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

Q9:

A car rental company charges $15 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 = 𝑑 + 1 5
  • C β„Ž = 1 5 𝑑
  • D 𝑑 = 1 5 βˆ’ β„Ž
  • E 𝑑 = 1 5 β„Ž

Q10:

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‘₯ + 𝑦 + 𝑐 + 𝑑
  • E 𝐢 = π‘₯ 𝑐 + 𝑦 𝑑

Q11:

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

Q12:

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

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

Q13:

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

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

Q14:

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

Q15:

Find the value of π‘₯ mentally given π‘₯+7π‘₯=3+73.

Q16:

The equation 𝑑=9𝑐 describes the total cost of buying packets of trading cards. The variable 𝑐 denotes the number of packs bought, and the variable 𝑑 represents the total cost in dollars. How much will Michael pay for 5 packs of cards?

Q17:

The equation β„Ž=4𝑑 describes the number of hours, β„Ž, that Olivia studies in 𝑑 days. How many hours does Olivia spend studying in 5 days?

Q18:

Solve the following equation mentally: 9𝑏=90.

Q19:

Is the equation 128=π‘š+14 true or false if π‘š=114?

  • Atrue
  • Bfalse

Q20:

Is the equation π‘₯+8=11 true or false if π‘₯=3?

  • Atrue
  • Bfalse

Q21:

Both Jacob and Elizabeth love to ride their motorbikes on the mountain roads. If Jacob rode 24 more miles than Elizabeth did, and he rode 38 miles in total, write an equation that describes the number of miles 𝑣 that Elizabeth rode.

  • A 𝑣 + 3 8 = 2 4
  • B 2 4 𝑣 = 3 8
  • C 𝑣 βˆ’ 2 4 = 3 8
  • D 3 8 𝑣 = 2 4
  • E 𝑣 + 2 4 = 3 8

Q22:

State whether the following statement is true or false: In π‘š+13=21, the variable π‘š can have any value and be a solution.

  • Atrue
  • Bfalse

Q23:

Which of the following equations is equivalent to the equation π‘₯βˆ’17=20?

  • A π‘₯ βˆ’ ( βˆ’ 1 7 ) = 2 0
  • B π‘₯ βˆ’ 1 7 = βˆ’ 2 0
  • C π‘₯ + ( βˆ’ 1 7 ) = 2 0
  • D π‘₯ βˆ’ ( βˆ’ 1 7 ) = βˆ’ 2 0

Q24:

Is the equation 26+28=𝑝 true or false if 𝑝=60?

  • Atrue
  • Bfalse

Q25:

Solve π‘₯+2=33+2.

  • A π‘₯ = 8
  • B π‘₯ = 3 3
  • C π‘₯ = 3 1
  • D π‘₯ = 3 5
  • E π‘₯ = 2

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