Here’s how to write an equation for each situation. The goal is to translate the word problem into a mathematical equation using the variable given.
---
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: 12 points
- Competing team: 8 points
- Difference: x = 12 – 8
✔ Equation: `x = 12 - 8`
*(You could also write `8 + x = 12`, which is equivalent and may be preferred depending on instruction.)*
---
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`
*(Simplified: `9 + n = 12`)*
---
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
- So: 6 + 7 + 4 + d = 20
✔ Equation: `6 + 7 + 4 + d = 20`
*(Simplified: `17 + d = 20`)*
---
4. The total earned from the lemonade stand was $60. The charge per cup was $2.00. There were l cups of lemonade sold.
- Total money = $60
- Price per cup = $2.00
- Number of cups = l
- So: 2 × l = 60
✔ Equation: `2l = 60`
---
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.
- Total boys = 20
- Each leader handles 7 boys
- Number of leaders needed = x
- So: 7 × x = 20? → Not quite — because you can’t have a fraction of a leader. But since this is algebra (not real-world rounding), we assume it’s asking for the *exact* relationship.
However, note: if there are 20 boys and 7 per group, you’d need 20 ÷ 7 ≈ 2.857 leaders — but you can’t have a fraction. In algebra problems like this, they usually want the equation that represents “total boys = 7 times number of leaders”, even if it doesn’t divide evenly.
✔ Equation: `7x = 20`
*(Note: In real life, you’d round up to 3 leaders, but since this is an algebra equation-writing exercise, `7x = 20` is correct.)*
---
6. Monica saved $20 for a new book. She paid d amount of money for the book and received $1.98 in change.
- Amount she had: $20
- Amount she paid: d
- Change received: $1.98
- So: 20 – d = 1.98
✔ Equation: `20 - d = 1.98`
---
✔ Final Answers:
1. `x = 12 - 8` or `8 + x = 12`
2. `6 + 3 + n = 12`
3. `6 + 7 + 4 + d = 20`
4. `2l = 60`
5. `7x = 20`
6. `20 - d = 1.98`
These equations model each situation using the variables provided. Let me know if you’d like to solve them too!
Parent Tip: Review the logic above to help your child master the concept of algebra problem worksheet.
