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:
- The distance from home to the beach is x miles.
- The return trip (from beach to home) is also x miles.
- So, total distance = x + x = 2x miles.
- We are told that the total distance is 56 miles.

So we write the equation:
$$
2x = 56
$$

Now 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:
- The cost of the ice cream cones = $24.
- Emily paid $m.
- She received $6 in change.
- That means:
$$
\text{Amount paid} - \text{Cost} = \text{Change}
$$
So:
$$
m - 24 = 6
$$

Now 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:
- Let $t$ = number of people in the morning.
- $\frac{1}{3}$ of them left, so $\frac{1}{3}t$ people left.
- Therefore, the number remaining = $t - \frac{1}{3}t = \frac{2}{3}t$
- We are told that after this, 30 people remained.

So:
$$
\frac{2}{3}t = 30
$$

Now solve for $t$:
Multiply both sides by 3:
$$
2t = 90
$$
Divide by 2:
$$
t = 45
$$

✔ Answer: $t = 45$

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✔ Final Answers:

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

Let me know if you'd like these written as equations or explained further!