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 |
|---|---|---|---|
| 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 |
|---|---|---|
| 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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