Question

quality landscaping co. contracts to put front yard sprinkler systems into each home in a new development. for each system installed in a yard, quality landscaping calculates that the supplies required are 14 10 - foot pvc pipes, 9 sprinkler heads, and a set of miscellaneous pvc parts. the project manager decides that he should also order 15 extra 10 - foot pvc pipes, sprinkler heads, and 4 extra sets of miscellaneous pvc parts. each 10 - foot pvc pipe costs $1.50, each sprinkler costs $2.50, and each set of pvc parts costs $15.
(a) write an equation for the total s the landscaping company will pay for the supplies needed to install sprinkler systems in y yards.
-select-
=
(b) if the company installs 18 sprinkler systems during the first phase of the development, how much will it cost for the supplies? (include units in your answer. more information
it will cost
for supplies.
(c) if the manager budgets $6006 for the entire project, how many sprinkler systems can be installed?
sprinkler systems can be installed.

Explanation:

Step1: Calculate cost for each item per yard

• For PVC pipes: Cost per yard for pipes is \((14y + 15)\times1.5\). The \(14y\) is for \(y\) yards (14 pipes per yard) and 15 extra pipes.
• For sprinkler heads: Cost per yard for heads is \((9y+6)\times2.5\). The \(9y\) is for \(y\) yards (9 heads per yard) and 6 extra heads.
• For PVC parts: Cost per yard for parts is \((y + 4)\times15\). The \(y\) is for \(y\) yards (1 set per yard) and 4 extra sets.

Step2: Expand each cost expression

• PVC pipes: \((14y + 15)\times1.5=21y+22.5\)
• Sprinkler heads: \((9y + 6)\times2.5 = 22.5y+15\)
• PVC parts: \((y + 4)\times15=15y + 60\)

Step3: Sum up the cost expressions

$$
LATEXBLOCK0
$$

Step4: Solve part (b)

Substitute \(y = 18\) into \(S=58.5y + 97.5\)

$$
LATEXBLOCK1
$$

Step5: Solve part (c)

Set \(S = 6006\) in \(S=58.5y+97.5\)

$$
LATEXBLOCK2
$$

Answer:

(a) \(S=58.5y + 97.5\)
(b) It will cost \(\$1150.5\) for supplies.
(c) \(101\) sprinkler systems can be installed.