Let’s solve each problem one by one.
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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 36 miles. Find x.
→ “To and from” means he went there (x miles) and came back (another x miles).
So total distance = x + x = 2x
We’re told that equals 36 miles.
Equation:
2x = 36
Now divide both sides by 2:
x = 36 ÷ 2
x = 18
✔ Check: If the beach is 18 miles away, going and coming back is 18 + 18 = 36. Correct!
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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.
→ She gave $m, spent $24, and got $6 back.
That means: money given – cost = change
So:
m – 24 = 6
Add 24 to both sides:
m = 6 + 24
m = 30
✔ Check: If she paid $30 and things cost $24, her change is $6. Correct!
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Problem 3:
In the morning, there were t people at the beach. Later at noon, ⅖ of the people left the beach and there were 30 people left on the beach. Find t.
→ If ⅖ left, then ⅗ are still there (because 1 – ⅖ = ⅗).
And we know ⅗ of t = 30.
Equation:
(3/5) × t = 30
To find t, multiply both sides by 5/3:
t = 30 × (5/3)
t = (30 ÷ 3) × 5
t = 10 × 5
t = 50
✔ Check: Start with 50 people. ⅖ of 50 = 20 leave. 50 – 20 = 30 left. Correct!
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Final Answer:
1. x = 18
2. m = 30
3. t = 50
Parent Tip: Review the logic above to help your child master the concept of pre algebra word problem worksheet.
