Word Problems Worksheets | Dynamically Created Word Problems - Free Printable

Let's solve each of these word problems step by step. I'll go through each one, set up the equations, and solve for the unknown number.

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1) A certain number was multiplied by 7. 4 was then taken away from the product. Finally, that difference was then divided by 9, resulting in 5. Find the initial number.

Let the initial number be $ x $.

Step-by-step:
- Multiply by 7: $ 7x $
- Subtract 4: $ 7x - 4 $
- Divide by 9: $ \frac{7x - 4}{9} = 5 $

Solve:
$$
\frac{7x - 4}{9} = 5 \\
7x - 4 = 45 \\
7x = 49 \\
x = 7
$$

✔ Answer: 7

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2) First, 33.25 was divided by some number. The resulting quotient was then multiplied by 7. Following this, 5.9 was subtracted from the product, giving 18.6. What was the initial divisor?

Let the divisor be $ x $.

Step-by-step:
- $ \frac{33.25}{x} $
- Multiply by 7: $ 7 \cdot \frac{33.25}{x} $
- Subtract 5.9: $ 7 \cdot \frac{33.25}{x} - 5.9 = 18.6 $

Solve:
$$
7 \cdot \frac{33.25}{x} = 18.6 + 5.9 = 24.5 \\
\frac{232.75}{x} = 24.5 \\
x = \frac{232.75}{24.5}
$$

Calculate:
$$
x = \frac{232.75}{24.5} = 9.5
$$

✔ Answer: 9.5

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3) 9 was added to a certain number. This sum was then divided by 3. Finally, the quotient was multiplied by 5. This product came out to 12. What was the number?

Let the number be $ x $.

Step-by-step:
- Add 9: $ x + 9 $
- Divide by 3: $ \frac{x + 9}{3} $
- Multiply by 5: $ 5 \cdot \frac{x + 9}{3} = 12 $

Solve:
$$
\frac{5(x + 9)}{3} = 12 \\
5(x + 9) = 36 \\
x + 9 = 7.2 \\
x = 7.2 - 9 = -1.8
$$

✔ Answer: -1.8

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4) 72 was divided by some number, then added to 12. Next, this difference was multiplied by 4, which gave a product of 12. Find this number.

Let the number be $ x $.

Step-by-step:
- $ \frac{72}{x} $
- Add to 12: $ \frac{72}{x} + 12 $
- Multiply by 4: $ 4 \left( \frac{72}{x} + 12 \right) = 12 $

Solve:
$$
4 \left( \frac{72}{x} + 12 \right) = 12 \\
\frac{72}{x} + 12 = 3 \\
\frac{72}{x} = -9 \\
x = \frac{72}{-9} = -8
$$

✔ Answer: -8

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5) Some number was divided by 6. After which, the quotient was added to 11. Next, the sum is multiplied by 6, which resulted in 60. Given this product, find the initial number.

Let the number be $ x $.

Step-by-step:
- $ \frac{x}{6} $
- Add 11: $ \frac{x}{6} + 11 $
- Multiply by 6: $ 6 \left( \frac{x}{6} + 11 \right) = 60 $

Solve:
$$
6 \cdot \frac{x}{6} + 6 \cdot 11 = 60 \\
x + 66 = 60 \\
x = 60 - 66 = -6
$$

✔ Answer: -6

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6) 10.3 was subtracted from a number. Then, that difference was multiplied by 7, after which that result was divided by 2.5. If the result of that division is -7, then what was the initial number?

Let the number be $ x $.

Step-by-step:
- $ x - 10.3 $
- Multiply by 7: $ 7(x - 10.3) $
- Divide by 2.5: $ \frac{7(x - 10.3)}{2.5} = -7 $

Solve:
$$
\frac{7(x - 10.3)}{2.5} = -7 \\
7(x - 10.3) = -17.5 \\
x - 10.3 = -2.5 \\
x = -2.5 + 10.3 = 7.8
$$

✔ Answer: 7.8

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7) Some number was divided into 176.9. This quotient was then multiplied by 4, after which the resulting product was added to 10.2. Given this sum totaled to -38.6, find the initial number.

"Divided into 176.9" means: $ \frac{176.9}{x} $

Let the number be $ x $.

Step-by-step:
- $ \frac{176.9}{x} $
- Multiply by 4: $ 4 \cdot \frac{176.9}{x} $
- Add 10.2: $ 4 \cdot \frac{176.9}{x} + 10.2 = -38.6 $

Solve:
$$
\frac{707.6}{x} = -38.6 - 10.2 = -48.8 \\
x = \frac{707.6}{-48.8} = -14.5
$$

✔ Answer: -14.5

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8) 0.2 was divided into a particular number. This quotient was then multiplied by 7, and 2.8 was taken from that product. If the previous operation resulted in -499.8, find the initial number.

"0.2 was divided into a number" → $ \frac{x}{0.2} $

Let the number be $ x $.

Step-by-step:
- $ \frac{x}{0.2} $
- Multiply by 7: $ 7 \cdot \frac{x}{0.2} $
- Subtract 2.8: $ 7 \cdot \frac{x}{0.2} - 2.8 = -499.8 $

Solve:
$$
7 \cdot \frac{x}{0.2} = -499.8 + 2.8 = -497 \\
\frac{x}{0.2} = \frac{-497}{7} = -71 \\
x = -71 \cdot 0.2 = -14.2
$$

✔ Answer: -14.2

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9) A particular number was divided by 5 and then 6 was taken away from that quotient. Finally, this difference was multiplied by 4. The product was -20. What was that number?

Let the number be $ x $.

Step-by-step:
- $ \frac{x}{5} $
- Subtract 6: $ \frac{x}{5} - 6 $
- Multiply by 4: $ 4 \left( \frac{x}{5} - 6 \right) = -20 $

Solve:
$$
\frac{4x}{5} - 24 = -20 \\
\frac{4x}{5} = 4 \\
4x = 20 \\
x = 5
$$

✔ Answer: 5

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10) 62.4 was divided by a particular number, then 2 was taken from the quotient. Afterwards, this difference was multiplied by 7, giving a product of -70. Find the particular number.

Let the number be $ x $.

Step-by-step:
- $ \frac{62.4}{x} $
- Subtract 2: $ \frac{62.4}{x} - 2 $
- Multiply by 7: $ 7 \left( \frac{62.4}{x} - 2 \right) = -70 $

Solve:
$$
\frac{62.4}{x} - 2 = -10 \\
\frac{62.4}{x} = -8 \\
x = \frac{62.4}{-8} = -7.8
$$

✔ Answer: -7.8

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✔ Final Answers:

1) 7
2) 9.5
3) -1.8
4) -8
5) -6
6) 7.8
7) -14.5
8) -14.2
9) 5
10) -7.8

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