# Worksheet: Introduction to Equations

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 and is 48.

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**Q4: **

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

Exercise | Push-ups | Sit-ups |
---|---|---|

Time (min) | 79 | ? |

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**Q5: **

Which of the following could be described by ?

- A passengers were on a bus. When 81 passengers got off the bus, there were 64 passengers left.
- B64 passengers were on a bus. When 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 .
- D 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.

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**Q7: **

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

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**Q8: **

If is 14 more than three times, which of the following must be true?

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**Q9: **

A car rental company charges per hour. Write an equation to represent this scenario using for the number of hours and for the total cost.

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**Q10: **

An animal shelter relies on donations to look after the cats and dogs. It costs to care for a cat and to care for a dog.

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

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

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**Q11: **

Michael can drive 65 miles in 5 hours. Write an equation to find the number of miles, , Michael can drive in hours.

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**Q12: **

The sum of two numbers, and , is 17. What is the mathematical relation between and ?

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**Q13: **

Which of the following means βThe difference between and five times is 19β?

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**Q14: **

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

(*Hint*: we may suppose that . Why?)

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**Q15: **

Find the value of mentally given .

**Q16: **

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

**Q17: **

The equation describes the number of hours, , that Chloe studies in days. How many hours does Chloe spend studying in 5 days?

**Q18: **

Solve the following equation mentally: .

**Q19: **

Is the equation true or false if ?

- Atrue
- Bfalse

**Q22: **

State whether the following statement is true or false: In , the variable can have any value and be a solution.

- Atrue
- Bfalse

**Q23: **

Which of the following equations is equivalent to the equation ?

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**Q24: **

Is the equation true or false if ?

- Atrue
- Bfalse

**Q25: **

Solve .

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