Answered

The Picketts have lived in their house for about 13 years. They like to keep a well-maintained property and have noticed that the paint on the exterior of their house is starting to peel. They get two bids for painting services from two different contractors. Based on the fee schedule below, which option would be the cheapest and by how much?




Handyman's Paint Service		Painting Plus Service

\$2250 all supplies and labor included for a 2-day job		Two day job estimate

\$300 preparation work

\$765 labor per day

\$225 paint and supplies





APainting Plus Service would be cheaper by $\$960$
BPainting Plus Service would be cheaper by $\$195$
CHandyman's Paint Service would be cheaper by $\$105$
DHandyman's Paint Service would be cheaper by $\$195$

Verified Answer :

  • The Handyman's Paint Service costs a total of \(\$2250\).
  • The Painting Plus Service costs \(\$300 + (\$765 \times 2) + \$225 = \$2055\).
  • The difference between the two costs is \(\$2250 - \$2055 = \$195\).
  • The Painting Plus Service is cheaper by \(\$195\), which is option b. \(\boxed{b}\)

Explanation

  1. Analyzing the Costs of Painting Services

To determine which painting service is more cost-effective for the Picketts, we first analyze the pricing structure for each contractor. The Handyman's Paint Service offers an all-inclusive fee of \(\$2250\) for a \(2\)-day job. The Painting Plus Service provides an estimate broken down by specific tasks: \(\$300\) for preparation, \(\$765\) per day for labor, and \(\$225\) for paint and supplies. Given the job duration is \(2\) days, we can calculate the total cost for each service and compare them.

  1. Calculating Total Costs for Each Service

For the Handyman's Paint Service, the total cost is explicitly given as \(\$2250\). For the Painting Plus Service, we calculate the total by summing the individual components over the \(2\)-day period:

  • Preparation: \(\$300\)
  • Labor: \(\$765 \times 2 = \$1530\)
  • Paint and Supplies: \(\$225\)

Summing these, the total cost for the Painting Plus Service is \(\$300 + \$1530 + \$225 = \$2055\).

  1. Comparing the Services and Concluding

Now that we have both total costs, we find the difference to determine which option is cheaper:

  • Difference: \(\$2250 - \$2055 = \$195\).

Since \(\$2055 < \$2250\), the Painting Plus Service is the more cost-effective choice, and it is cheaper by \(\$195\). This corresponds to option (b).

Examples

When planning home maintenance or any large project, comparing competing estimates is a fundamental skill. Just like the Picketts, homeowners frequently encounter contractors who charge flat rates versus those who provide itemized bills. Being able to correctly calculate and compare these totals ensures you make the most budget-conscious decision, allowing you to allocate your resources effectively toward other household needs.

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