Math worksheet featuring ten algebraic word problems for solving unknown numbers through various arithmetic operations.

Let’s solve each word problem step by step. We’ll work backwards from the final result to find the original number, since each problem describes a sequence of operations that lead to a known answer.

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

Start from the end:
Final result = 5
Before dividing by 9 → multiply 5 × 9 = 45
Before subtracting 4 → add 4 → 45 + 4 = 49
Before multiplying by 7 → divide by 7 → 49 ÷ 7 = 7

✔ Initial number = 7

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Problem 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?

Start from the end:
Final result = 18.6
Before subtracting 5.9 → add 5.9 → 18.6 + 5.9 = 24.5
Before multiplying by 7 → divide by 7 → 24.5 ÷ 7 = 3.5
This is the quotient after dividing 33.25 by the unknown divisor.
So, 33.25 ÷ ? = 3.5 → ? = 33.25 ÷ 3.5

Calculate:
33.25 ÷ 3.5 = (multiply numerator and denominator by 10) → 332.5 ÷ 35
35 × 9 = 315 → 332.5 - 315 = 17.5 → 35 × 0.5 = 17.5 → so 9.5

✔ Initial divisor = 9.5

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Problem 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 5. What was the number?

Start from the end:
Final result = 5
Before multiplying by 5 → divide by 5 → 5 ÷ 5 = 1
Before dividing by 3 → multiply by 3 → 1 × 3 = 3
Before adding 9 → subtract 9 → 3 - 9 = -6

✔ Number = -6

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Problem 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.

Wait — “added to 12” then “this difference”? That wording is confusing. Let’s read carefully:

“72 was divided by some number, then added to 12.” → So: (72 ÷ x) + 12
Then: “this difference was multiplied by 4” — but it’s a sum, not a difference. Probably typo or miswording. Likely means “this result”.

Assume: [(72 ÷ x) + 12] × 4 = 12

Solve:
Divide both sides by 4 → (72 ÷ x) + 12 = 3
Subtract 12 → 72 ÷ x = 3 - 12 = -9
So, 72 ÷ x = -9 → x = 72 ÷ (-9) = -8

✔ Number = -8

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

Start from the end:
Final result = 60
Before multiplying by 5 → divide by 5 → 60 ÷ 5 = 12
Before adding 11 → subtract 11 → 12 - 11 = 1
Before dividing by 6 → multiply by 6 → 1 × 6 = 6

✔ Initial number = 6

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Problem 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?

Start from the end:
Final result = -7
Before dividing by 2.5 → multiply by 2.5 → -7 × 2.5 = -17.5
Before multiplying by 7 → divide by 7 → -17.5 ÷ 7 = -2.5
Before subtracting 10.3 → add 10.3 → -2.5 + 10.3 = 7.8

✔ Initial number = 7.8

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Problem 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 totalled to -38.6, find the initial number.

Note: “divided into” usually means 176.9 ÷ x (not x ÷ 176.9). In math, “A divided into B” often means B ÷ A. But let’s check context.

It says: “Some number was divided into 176.9” → likely means 176.9 ÷ x.

Then: (176.9 ÷ x) × 4 + 10.2 = -38.6

Solve:
Subtract 10.2 → (176.9 ÷ x) × 4 = -38.6 - 10.2 = -48.8
Divide by 4 → 176.9 ÷ x = -48.8 ÷ 4 = -12.2
So, 176.9 ÷ x = -12.2 → x = 176.9 ÷ (-12.2)

Calculate:
176.9 ÷ 12.2 ≈ ?
12.2 × 14 = 170.8 → 176.9 - 170.8 = 6.1 → 12.2 × 0.5 = 6.1 → so 14.5
Thus, 176.9 ÷ 12.2 = 14.5 → so with negative sign: x = -14.5

✔ Initial number = -14.5

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Problem 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 particular number” → means: number ÷ 0.2

Let number be x → (x ÷ 0.2) × 7 - 2.8 = -499.8

Solve:
Add 2.8 → (x ÷ 0.2) × 7 = -499.8 + 2.8 = -497
Divide by 7 → x ÷ 0.2 = -497 ÷ 7 = -71
Multiply by 0.2 → x = -71 × 0.2 = -14.2

✔ Initial number = -14.2

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Problem 9:
A particular number was divided by 5 and then 6 was taken away from that quotient. Finally, this difference was multiplied by 4. Given the product was -20, what was that number?

Start from the end:
Final result = -20
Before multiplying by 4 → divide by 4 → -20 ÷ 4 = -5
Before subtracting 6 → add 6 → -5 + 6 = 1
Before dividing by 5 → multiply by 5 → 1 × 5 = 5

✔ Number = 5

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Problem 10:
82.4 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 number be x → [(82.4 ÷ x) - 2] × 7 = -70

Solve:
Divide by 7 → (82.4 ÷ x) - 2 = -70 ÷ 7 = -10
Add 2 → 82.4 ÷ x = -10 + 2 = -8
So, x = 82.4 ÷ (-8) = -10.3

✔ Particular number = -10.3

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Final Answer:
1) 7
2) 9.5
3) -6
4) -8
5) 6
6) 7.8
7) -14.5
8) -14.2
9) 5
10) -10.3