Variables and equations word problem worksheets | Worsheets library - Free Printable

Let's solve each of the three word problems step by step, using variables and equations.

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Problem 1:

The beach is x miles away from home. Josh drove to and from the beach with a total distance of 56 miles. Find x.

#### Step-by-step Solution:
- Distance from home to beach = $ x $ miles
- Distance from beach back to home = $ x $ miles
- Total round trip distance = $ x + x = 2x $
- We are told that the total distance is 56 miles:
$$
2x = 56
$$
- Solve for $ x $:
$$
x = \frac{56}{2} = 28
$$

✔ Answer: $ x = 28 $ miles

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Problem 2:

Emily bought some ice cream cones which cost $24. She paid $m and got back $6 of change. Find m.

#### Step-by-step Solution:
- Cost of ice cream cones = $24
- Amount she paid = $ m $
- Change received = $6
- So, the amount paid minus the cost equals the change:
$$
m - 24 = 6
$$
- Solve for $ m $:
$$
m = 6 + 24 = 30
$$

✔ Answer: $ m = 30 $

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Problem 3:

In the morning, there were t people at the beach. Later at noon, $ \frac{1}{3} $ of the people left the beach and there were 30 people left on the beach. Find t.

#### Step-by-step Solution:
- Initial number of people = $ t $
- $ \frac{1}{3} $ of the people left, so $ \frac{1}{3}t $ people left
- Number of people remaining = $ t - \frac{1}{3}t = \frac{2}{3}t $
- We are told that 30 people remained:
$$
\frac{2}{3}t = 30
$$
- Solve for $ t $:
$$
t = 30 \times \frac{3}{2} = 45
$$

✔ Answer: $ t = 45 $

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✔ Final Answers:

1. $ x = 28 $
2. $ m = 30 $
3. $ t = 45 $

These solutions use algebraic equations based on the given information in each word problem.