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Matt is writing an estimate for a client who would like to have a patio built from interlocking blocks. The landscaper has provided two designs that would fit in the yard:Plan 1 is for a patio 3 yards long and 4 yards wide.Plan 2 is for a patio 5 yards long and 2.5 yards wide.The client wants to know how much each plan will cost. Matt will use rectangular bricks that measure 8" by 4" and cost $5.00 a square foot. Matt's labor charge is $8.50 per square foot.1) What is the total cost of plan 2?(Enter your dollars and cents with no dollar symbol.)2) Which plan is the least expensive? Enter plan 1 or plan 2

Question

Matt is writing an estimate for a client who would like to have a patio built from interlocking blocks. The landscaper has provided two designs that would fit in the yard:Plan 1 is for a patio 3 yards long and 4 yards wide.Plan 2 is for a patio 5 yards long and 2.5 yards wide.The client wants to know how much each plan will cost. Matt will use rectangular bricks that measure 8" by 4" and cost 5.00asquarefoot.Mattslaborchargeis5.00 a square foot. Matt's labor charge is 8.50 per square foot.1) What is the total cost of plan 2?(Enter your dollars and cents with no dollar symbol.)2) Which plan is the least expensive? Enter plan 1 or plan 2

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Solution

To answer these questions, we first need to calculate the area of each patio in square feet, since the cost of materials and labor is given per square foot.

1 yard = 3 feet

Plan 1: The patio is 3 yards long and 4 yards wide. Convert these measurements to feet: Length = 3 yards * 3 feet/yard = 9 feet Width = 4 yards * 3 feet/yard = 12 feet So, the area of the patio for Plan 1 is Length * Width = 9 feet * 12 feet = 108 square feet.

Plan 2: The patio is 5 yards long and 2.5 yards wide. Convert these measurements to feet: Length = 5 yards * 3 feet/yard = 15 feet Width = 2.5 yards * 3 feet/yard = 7.5 feet So, the area of the patio for Plan 2 is Length * Width = 15 feet * 7.5 feet = 112.5 square feet.

Next, calculate the total cost for each plan. The total cost includes the cost of materials (5.00persquarefoot)andlabor(5.00 per square foot) and labor (8.50 per square foot), so the total cost per square foot is 5.00+5.00 + 8.50 = $13.50.

  1. The total cost of Plan 2 is the area of the patio * total cost per square foot = 112.5 square feet * 13.50/squarefoot=13.50/square foot = 1518.75.

  2. To find out which plan is the least expensive, calculate the total cost for Plan 1: The total cost of Plan 1 is the area of the patio * total cost per square foot = 108 square feet * 13.50/squarefoot=13.50/square foot = 1458.00.

So, Plan 1 is the least expensive.

This problem has been solved

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