1. Let \( h \) be the number of hours Carl worked last week.
- Equation: \( 8h + 68 = 404 \)
- Subtract 68 from both sides: \( 8h = 336 \)
- Divide by 8: \( h = 42 \)
- Carl worked 42 hours last week.
2. Let \( s \) be the original price of each sketchbook.
- Equation: \( 6(s - 1) = 24 \)
- Divide both sides by 6: \( s - 1 = 4 \)
- Add 1 to both sides: \( s = 5 \)
- The original price of each sketchbook was $5.
3. Let \( t \) be the original price of each ticket.
- Equation: \( 8(t - 2) = 120 \)
- Divide both sides by 8: \( t - 2 = 15 \)
- Add 2 to both sides: \( t = 17 \)
- The original price of each ticket was $17.
4. Let \( s \) be the number of scarves Elena sold.
- Equation: \( 12s - 90 = 210 \)
- Add 90 to both sides: \( 12s = 300 \)
- Divide by 12: \( s = 25 \)
- Elena sold 25 scarves.
5. Let \( p \) be the price of each video game before tax.
- Equation: \( 3(p + 1.25) = 107 \)
- Divide both sides by 3: \( p + 1.25 = \frac{107}{3} \approx 35.67 \)
- Subtract 1.25: \( p \approx 34.42 \)
- The price of each video game before tax was approximately $34.42.
6. Let \( m \) be the number of months.
- Equation: \( 18.25m + 75.00 = 305.75 \)
- Subtract 75.00 from both sides: \( 18.25m = 230.75 \)
- Divide by 18.25: \( m = 12.64 \)
- Since months must be whole numbers, and paying for part of a month is unlikely, this suggests an error in the problem setup or interpretation. However, solving algebraically gives approximately 12.64 months. For practical purposes, it might imply 13 months if partial months are rounded up, but strictly mathematically, it's 12.64. Given the context, it’s likely intended to be a whole number, so rechecking the problem may be needed. But based on calculation: approximately 12.64 months.
Parent Tip: Review the logic above to help your child master the concept of algebra word problems worksheet with answers.
