In this worksheet, we will practice reading and writing algebraic equations, clarifying this concept through tables, and applying it in real-life situations and word problems.

**Q1: **

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

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**Q5: **

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

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

Time (min) | 79 | ? |

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**Q8: **

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.
- B passengers were on a bus. When 64 passengers got off the bus, there were 81 passengers left.
- C64 passengers were on a bus. When 81 passengers joined them, the total was .
- D64 passengers were on a bus. When passengers got on the bus, the total number of passengers was 81.

**Q9: **

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

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**Q10: **

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

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**Q11: **

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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**Q12: **

The table shows the results of a survey which asked a group of students to pick their favourite 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 |
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Fraction of Students |

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**Q13: **

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

Item | Regular Price | Sale Price |
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A | $17.00 | $9.35 |

B | $19.00 | $10.45 |

C | $13.00 | $7.15 |

D | $20.00 | $11.00 |

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**Q14: **

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

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**Q15: **

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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**Q16: **

Rania 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 Rania gave the cashier, and then solve it.

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**Q17: **

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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**Q18: **

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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**Q19: **

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

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**Q20: **

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.

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**Q21: **

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

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**Q22: **

Dina 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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