Let’s solve each problem step by step.
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Problem 1:
> Five times a number increased by seven is equal to forty-seven. What is the number?
Step 1: Let the unknown number be
x.
Step 2: “Five times a number” → 5x
“Increased by seven” → 5x + 7
“Is equal to forty-seven” → 5x + 7 = 47
Step 3: Solve for x.
Subtract 7 from both sides:
5x = 47 - 7
5x = 40
Divide both sides by 5:
x = 40 ÷ 5
x = 8
✔ Check: 5 × 8 = 40; 40 + 7 = 47 → Correct.
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Problem 2:
> The sum of two consecutive integers is sixty-five. Find the two numbers.
Step 1: Consecutive integers mean one after another, like 5 and 6, or 10 and 11.
Let the first integer be
n.
Then the next consecutive integer is
n + 1.
Step 2: Their sum is 65:
n + (n + 1) = 65
Simplify:
2n + 1 = 65
Subtract 1 from both sides:
2n = 64
Divide by 2:
n = 32
So the two numbers are:
32 and 33
✔ Check: 32 + 33 = 65 → Correct.
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Problem 3:
> Ninety-six golf balls were picked up at the driving range and placed into two buckets. One bucket has twenty-eight more balls than the other bucket. How many golf balls are in each bucket?
Step 1: Let the smaller bucket have
x balls.
Then the larger bucket has
x + 28 balls.
Step 2: Total balls = 96
So:
x + (x + 28) = 96
Simplify:
2x + 28 = 96
Subtract 28 from both sides:
2x = 68
Divide by 2:
x = 34
So the smaller bucket has 34 balls.
The larger bucket has 34 + 28 = 62 balls.
✔ Check: 34 + 62 = 96 → Correct.
Also, 62 - 34 = 28 → Correct difference.
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Final Answer:
Problem 1: 8
Problem 2: 32 and 33
Problem 3: 34 and 62
Parent Tip: Review the logic above to help your child master the concept of algebra 1 word problems worksheet.
