A Tampines delivery service charges $(3.50 + 0.80d + 1.50w)$ dollars per parcel, where $d$ is the distance travelled (in km) and $w$ is the parcel weight (in kg). For a particular parcel, the expression simplifies to $(3.50 + 0.80d + 7.50)$ dollars. What does this simplified expression represent?
Show Worked Solution
Worked Solution
Step 1: Compare the two expressions. Original: $3.50 + 0.80d + 1.50w$. Simplified: $3.50 + 0.80d + 7.50$.\n
Step 2: Identify what changed. The first two terms ($3.50$ and $0.80d$) are IDENTICAL in both. Only the $1.50w$ term has been replaced by $7.50$.\n
Step 3: Solve for the substituted value. $1.50w = 7.50$ implies $w = 7.50 \\div 1.50 = 5$. So the substitution is $w = 5$ kg.\n
Step 4: Interpret what this means in context. $w = 5$ kg means the parcel weight has been fixed at $5$ kg. The variable $d$ is UNCHANGED, meaning the distance is still unknown.\n
Step 5: Conclusion. The simplified expression gives the total delivery cost in dollars for any parcel weighing $5$ kg, with the distance $d$ still to be substituted later.\nCheck: Substitute $w = 5$ into the original: $3.50 + 0.80d + 1.50(5) = 3.50 + 0.80d + 7.50$ ✓.
Answer: The total delivery cost in dollars for a parcel weighing 5 kg, with the distance still unknown.
Correct answer: The total delivery cost in dollars for a parcel weighing 5 kg, with the distance still unknown.
Want more questions like this? Superholic Lab has 10,000+ MOE-aligned questions with full worked solutions.
Start Free Trial — 7 Days Free