SOLUTION: Algebra word problems worksheet 1 number problems ... - Free Printable

Let's solve each of the three algebra word problems 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: Define the variable
Let the unknown number be $ x $.

#### Step 2: Translate the words into an equation
"Five times a number" → $ 5x $
"Increased by seven" → $ 5x + 7 $
"Is equal to forty-seven" → $ = 47 $

So, the equation is:
$$
5x + 7 = 47
$$

#### Step 3: Solve for $ x $
Subtract 7 from both sides:
$$
5x = 47 - 7 = 40
$$

Divide both sides by 5:
$$
x = \frac{40}{5} = 8
$$

#### ✔ Answer:
The number is 8.

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Problem 2)

The sum of two consecutive integers is sixty-five. Find the two numbers.

#### Step 1: Define the variables
Let the first integer be $ x $.
Then the next consecutive integer is $ x + 1 $.

#### Step 2: Set up the equation
Their sum is 65:
$$
x + (x + 1) = 65
$$

Simplify:
$$
2x + 1 = 65
$$

#### Step 3: Solve for $ x $
Subtract 1 from both sides:
$$
2x = 64
$$

Divide by 2:
$$
x = 32
$$

So the two consecutive integers are:
- $ x = 32 $
- $ x + 1 = 33 $

#### ✔ Answer:
The two numbers are 32 and 33.

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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: Define the variables
Let the number of golf balls in the smaller bucket be $ x $.
Then the larger bucket has $ x + 28 $ balls.

#### Step 2: Set up the equation
Total balls = 96:
$$
x + (x + 28) = 96
$$

Simplify:
$$
2x + 28 = 96
$$

#### Step 3: Solve for $ x $
Subtract 28 from both sides:
$$
2x = 68
$$

Divide by 2:
$$
x = 34
$$

So:
- Smaller bucket: $ x = 34 $
- Larger bucket: $ x + 28 = 62 $

#### ✔ Answer:
One bucket has 34 golf balls, and the other has 62 golf balls.

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✔ Final Answers:

1. 8
2. 32 and 33
3. 34 and 62

Let me know if you'd like these explained visually or with diagrams!