Simple Algebra Word Problems worksheet with six scenarios for writing equations.

Let's solve each of these algebra word problems by writing an equation for each situation. We'll go step by step and explain the reasoning.

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1. Glenn’s soccer team won the game scoring 12 points to 8. His team scored x more points than the competing team.

- Glenn's team scored 12 points.
- The competing team scored 8 points.
- The difference in points is $ x $, so:

$$
12 - 8 = x
$$

✔ Equation:
$$
x = 12 - 8
$$

Or simplified:
$$
x = 4
$$

> *Explanation:* The problem asks for an equation showing how many more points Glenn’s team scored. So, subtract the opponent's score from Glenn’s team score.

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2. Danya had a case of 12 bottles of fingernail polish. She had 6 different shades of pink, 3 shades of purple and n shades of green.

- Total bottles = 12
- Pink: 6
- Purple: 3
- Green: $ n $

So:
$$
6 + 3 + n = 12
$$

✔ Equation:
$$
6 + 3 + n = 12
$$

> *Explanation:* Add up all the known and unknown shades to equal the total number of bottles.

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3. Larry ran a dog kennel with 20 dogs. He had 6 beagles, 7 collies, 4 pekinese and d poodles.

- Total dogs = 20
- Beagles: 6
- Collies: 7
- Pekinese: 4
- Poodles: $ d $

Add them:
$$
6 + 7 + 4 + d = 20
$$

✔ Equation:
$$
6 + 7 + 4 + d = 20
$$

> *Explanation:* Sum of all breeds equals total number of dogs.

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4. The total earned from the lemonade stand was $60. The charge per cup was $2.00. There were l cups of lemonade sold.

- Price per cup: $2.00
- Number of cups sold: $ l $
- Total earnings: $60

So:
$$
2l = 60
$$

✔ Equation:
$$
2l = 60
$$

> *Explanation:* Multiply price per cup by number of cups sold to get total money earned.

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5. Darien counted 20 other boys in his cub scout den. The camping trip requires a den leader for each group of seven boys. The trip required x number of leaders.

- Number of boys: 20
- Each group has 7 boys
- Number of leaders needed: $ x $

To find how many groups of 7 can be made from 20 boys:
$$
x = \frac{20}{7}
$$

But since we're looking for the number of leaders (groups), and it must be a whole number (you can't have a fraction of a leader), but the problem asks for an equation — not necessarily solving it.

So:
$$
x = \left\lceil \frac{20}{7} \right\rceil
$$

However, if we are only writing an equation without rounding (and assuming that the number of leaders is based on full groups), then:

$$
7x = 20
$$

But this would imply $ x = 20/7 $, which isn't a whole number. But since you need one leader per group of 7, and you can't have partial leaders, we usually use ceiling function.

But since this is simple algebra, likely they want:
$$
x = \frac{20}{7}
$$

Wait — better approach: If there are 20 boys, and every 7 boys need 1 leader, then:

$$
\text{Number of leaders} = \frac{\text{Total boys}}{7}
$$

So:
$$
x = \frac{20}{7}
$$

But again, this gives a decimal.

Alternatively, if we assume that each group of 7 boys needs 1 leader, then the number of groups is $ x $, and total boys is $ 7x $. But here, total boys is 20.

So:
$$
7x = 20
$$

But that doesn’t make sense because 7x = 20 → x ≈ 2.86, not whole.

But perhaps the question means: "There are 20 boys, and each group has 7 boys, so how many leaders are needed?"

Then the correct equation is:
$$
x = \left\lceil \frac{20}{7} \right\rceil
$$

But since this is simple algebra, maybe they expect:
$$
7x = 20
$$

But that’s not accurate.

Wait — actually, let's re-read:

> "The camping trip requires a den leader for each group of seven boys."

So, each group of 7 boys gets one leader.

So total number of leaders $ x $ is the number of such groups.

So:
$$
x = \frac{20}{7}
$$

But again, fractional leaders don't make sense.

However, in algebra word problems like this, sometimes they just want the relationship, even if it's not integer.

So best equation is:
$$
x = \frac{20}{7}
$$

But that seems odd.

Alternatively, maybe the total number of boys is divided into groups of 7, so:

$$
7x = 20
$$

But that implies 20 = 7x → x = 20/7

So either way, the equation is:

✔ Equation:
$$
7x = 20
$$

> *Explanation:* Each leader oversees 7 boys, so total boys = 7 × number of leaders.

Even though it results in a fraction, the equation models the situation.

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6. Monica saved $20 for a new book. She paid d amount of money for the book and received $1.98 in change.

- She started with $20
- Paid $d for the book
- Got $1.98 back

So:
$$
20 - d = 1.98
$$

✔ Equation:
$$
20 - d = 1.98
$$

> *Explanation:* Money she had minus cost of book equals change received.

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✔ Final Answers:

1. $ x = 12 - 8 $
2. $ 6 + 3 + n = 12 $
3. $ 6 + 7 + 4 + d = 20 $
4. $ 2l = 60 $
5. $ 7x = 20 $
6. $ 20 - d = 1.98 $

Let me know if you'd like these simplified or solved!