Real-Life Equations: Crafting Word Problems with Diagrams

1. Sarah has 5 apples. She buys x more apples. Write an equation to represent the total number of apples Sarah has now. What is the word problem that corresponds to this equation?

• Sarah has 5 apples and gives away x apples.

• Sarah has 5 apples and buys 2 more apples.

• Sarah has a total of 5 + x apples after buying x more apples.

• Sarah has a total of 5 - x apples after giving away x apples.

2. A rectangle has a length of 10 cm and a width of w cm. Write an equation for the perimeter of the rectangle. Create a word problem that describes this situation.

• P = 2(10 + w) cm. A word problem could be: 'A gardener is designing a rectangular flower bed that is 10 cm long. If the width of the flower bed is w cm, what is the formula for the perimeter of the flower bed?'.

• P = 2(10 - w) cm. A word problem could be: 'A painter is creating a rectangular canvas that is 10 cm long. If the width of the canvas is w cm, what is the formula for the perimeter of the canvas?'.

• P = 2(10 + 5) cm. A word problem could be: 'A chef is designing a rectangular table that is 10 cm long. If the width of the table is 5 cm, what is the formula for the perimeter of the table?'

• P = 10w cm. A word problem could be: 'A farmer is building a fence around a rectangular plot that is 10 cm wide. If the length of the plot is w cm, what is the formula for the perimeter of the plot?'.

3. Tom is 12 years old. His sister is y years younger than him. Write an equation to express Tom's sister's age. What word problem can you create from this equation?

• Tom's sister's age can be expressed as 12 - y. A word problem could be: 'Tom is 12 years old. If his sister is y years younger than him, how old is she?'.

• Tom's sister's age can be expressed as y - 12.

• Tom's sister's age can be expressed as 12 + y.

• A word problem could be: 'Tom is 12 years old. If his sister is y years older than him, how old is she?'.

4. A car travels at a speed of 60 miles per hour for t hours. Write an equation for the distance traveled. How would you describe this situation in a word problem?

• distance = 60t

• distance = 60/t

• distance = 60t^2

• distance = 60 + t

5. A box contains 20 chocolates. If x chocolates are eaten, how many are left? Write the equation and create a word problem that fits this scenario.

• 20 - x

• 20 + x

• 20 * x

• x - 20

6. The total cost of 3 notebooks and y pencils is $15. Write an equation to represent this situation. What word problem can you derive from this equation?

• 3x + 2z = 10; What is the total cost of 3 notebooks and 2 pencils?

• 2x + 5z = 15; How many notebooks can you buy for $15?

• 4x + 3z = 15; If each notebook costs x dollars, how much do 5 notebooks and 2 pencils cost?

• 3x + yz = 15; A word problem could be: 'If each notebook costs x dollars and each pencil costs z dollars, how many pencils can you buy if you purchase 3 notebooks for a total of $15?'.

7. A farmer has 50 apples and he sells s apples. Write an equation to show how many apples he has left. Create a word problem that illustrates this situation.

• 50 - s

• s - 50

• 50 + s

• 50 - s + 10

8. A swimming pool is filled with 200 liters of water. If x liters are added each hour, write an equation for the total amount of water after h hours. What word problem corresponds to this equation?

• Total water = 200 - x * h; A word problem could be: 'A swimming pool starts with 200 liters of water. If x liters of water are removed every hour, how much water will be in the pool after h hours?'.

• Total water = 200 + x; A word problem could be: 'A swimming pool starts with 200 liters of water. If x liters of water are added once, how much water will be in the pool?'.

• Total water = 200 + x * 2h; A word problem could be: 'A swimming pool starts with 200 liters of water. If x liters of water are added every two hours, how much water will be in the pool after h hours?'

• Total water = 200 + x * h; A word problem could be: 'A swimming pool starts with 200 liters of water. If x liters of water are added every hour, how much water will be in the pool after h hours?'.

9. A book costs $10 and you buy b books. Write an equation for the total cost. Create a word problem that describes this purchase.

• Total Cost = 5b. A word problem could be: If John buys b books for $5 each, how much will he spend?

• Total Cost = 10b. A word problem could be: If Sarah wants to buy b books for her new class and each book costs $10, how much will she spend in total?

• Total Cost = 15b. A word problem could be: If Emily buys b books for $15 each, what is her total cost?

• Total Cost = 10 + b. A word problem could be: If Mark buys b books and pays an extra $10, what is his total cost?

10. A train leaves the station at 3 PM and travels at a speed of 80 km/h for t hours. Write an equation for the distance traveled by the train. What word problem can you create based on this equation?

• A train departs at 4 PM and travels at 60 km/h. How far will it go by 6 PM?

• A train leaves the station at 2 PM and travels at 100 km/h. What is the distance after 3 hours?

• A train starts at 3 PM and moves at 80 km/h. How long will it take to travel 160 km?

• A train leaves the station at 3 PM and travels at a speed of 80 km/h. How far will the train have traveled by 5 PM?