1. Let the width be $w$ meters. Then the length is $3w + 12$ meters.
Perimeter formula: $2(\text{length} + \text{width}) = 200$
Substitute: $2((3w + 12) + w) = 200$
Simplify: $2(4w + 12) = 200$
Divide by 2: $4w + 12 = 100$
Subtract 12: $4w = 88$
Divide by 4: $w = 22$
Length: $3(22) + 12 = 66 + 12 = 78$
Width is 22 m, length is 78 m.
2. Let $x$ be the amount invested at 5%. Then $35000 - x$ is invested at 3%.
Total interest: $0.05x + 0.03(35000 - x) = 1250$
Distribute: $0.05x + 1050 - 0.03x = 1250$
Combine like terms: $0.02x + 1050 = 1250$
Subtract 1050: $0.02x = 200$
Divide by 0.02: $x = 10000$
Amount at 5%: P10,000
Amount at 3%: P35,000 - P10,000 = P25,000
3. Let $t$ be the time in hours until they meet.
Distance covered by Bus A: $75t$ km
Distance covered by Bus B: $85t$ km
Total distance covered when they meet: $75t + 85t = 560$
Combine: $160t = 560$
Divide: $t = 560 / 160 = 3.5$
They meet after 3.5 hours.
4. Let $t$ be the time in hours after 8:00 AM.
Distance covered by first car: $72t$ km
Distance covered by second car: $63t$ km
Total distance apart: $72t + 63t = 540$
Combine: $135t = 540$
Divide: $t = 540 / 135 = 4$
Time: 8:00 AM + 4 hours = 12:00 PM
First car traveled: $72 \times 4 = 288$ km
Second car traveled: $63 \times 4 = 252$ km
Parent Tip: Review the logic above to help your child master the concept of using equations to solve word problems worksheet.
