Sure! Here are five word problems that involve turning statements into equations, along with their solutions. These examples will cover different types of problems where you need to create equations based on the given information.

Problem 1: Cost of Apples

Word Problem: A bag of apples costs $3 per apple. If you buy $x$ apples, the total cost is $36. Write an equation to represent this situation and solve for $x$.

Equation: $3x = 36$

Solution: $x = \frac{36}{3} = 12$

So, you bought 12 apples.

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Problem 2: Distance Travelled

Word Problem: A car travels at a speed of 60 miles per hour. If the car travels for $t$ hours, the total distance travelled is 180 miles. Write an equation to represent this situation and solve for $t$.

Equation: $60t = 180$

Solution: $t = \frac{180}{60} = 3$

The car travelled for 3 hours.

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Problem 3: Tickets Sold

Word Problem: The price of each ticket to a concert is $20. If $n$ tickets are sold, the total revenue is $800. Write an equation to represent this situation and solve for $n$.

Equation: $20n = 800$

Solution: $n = \frac{800}{20} = 40$

So, 40 tickets were sold.

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Problem 4: Mixing Solutions

Word Problem: You are mixing two solutions. The first solution is 60% alcohol, and the second is 40% alcohol. If you mix 3 liters of the first solution with $x$ liters of the second solution, and the final mixture is 50% alcohol, write an equation to represent the amount of alcohol in the mixture, and solve for $x$.

Equation: $0.60(3) + 0.40(x) = 0.50(3 + x)$

Solution: $1.8 + 0.40x = 1.5 + 0.50x$

$1.8 - 1.5 = 0.50x - 0.40x$

$0.3 = 0.10x$

$x = \frac{0.3}{0.10} = 3$

So, 3 liters of the second solution were mixed.

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Problem 5: Age Problem

Word Problem: Emily is 5 years older than twice her sister's age. If Emily is $E$ years old and her sister is $S$ years old, write an equation to represent their ages, and solve for $E$ when $S = 10$.

Equation: $E = 2S + 5$

Solution: When $S = 10$: $E = 2(10) + 5 = 20 + 5 = 25$

Emily is 25 years old.

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Tips:

• Read carefully: Always look for key phrases like "total", "per", "is", or "more than" that help identify the equation structure.
• Units matter: Make sure you are consistent with the units (miles, hours, dollars, etc.).
• Simplify step-by-step: Don't rush solving the equation; simplify it in steps.

Would you like more examples or any further explanation? Here are a few related questions:

1. Can you solve a word problem involving the area of a rectangle?
2. How can you set up an equation for the total cost of multiple items with different prices?
3. How would you approach a problem that involves proportions and ratios?
4. What are some tricks to identify the variable in word problems?
5. Could you solve a problem involving a savings account with interest?