Copper pipe costs \(x\) cents per foot in \(8\)-foot lengths, and \(x + y\) cents per foot in shorter lengths. What is

[M7MBA]

Copper pipe costs \(x\) cents per foot in \(8\)-foot lengths, and \(x + y\) cents per foot in shorter lengths. What is the lowest possible price, in cents, of \(51\) feet of pipe in terms of \(x\) and \(y?\)

A. \(51(x + y)\)
B. \(51x\)
C. \(48x + 3y\)
D. \(48(x + y)\)
E. \(51x + 3y\)

Answer: E

Source: Princeton Review

[swerve]

Copper pipe costs \(x\) cents per foot in \(8\)-foot lengths, and \(x + y\) cents per foot in shorter lengths. What is the lowest possible price, in cents, of \(51\) feet of pipe in terms of \(x\) and \(y?\)

A. \(51(x + y)\)
B. \(51x\)
C. \(48x + 3y\)
D. \(48(x + y)\)
E. \(51x + 3y\)

Answer: E

Source: Princeton Review

\(51=8 \cdot 6 + 3\)

So we need \(6\) bars of \(8\)-foot length, which costs \(48x\) and \(3\)-foot shorter bars, which costs \(3(x+y)\)

\(48x+3(x+y)=51x+3y\Longrightarrow\) E

[jhavyom]

Copper pipe costs \(x\) cents per foot in \(8\)-foot lengths, and \(x + y\) cents per foot in shorter lengths. What is the lowest possible price, in cents, of \(51\) feet of pipe in terms of \(x\) and \(y?\)

A. \(51(x + y)\)
B. \(51x\)
C. \(48x + 3y\)
D. \(48(x + y)\)
E. \(51x + 3y\)

Answer: E

Source: Princeton Review

51 foot = 48 foot + 3 foot
Since 48 is a multiple of 8, price for 48 foot = 48x
Now, price for remaining 3 foot, 3(x+y)

Total cost = 48x + 3(x+y) = 51x + 3y

Choice E is the answer.

[Scott@TargetTestPrep]

Copper pipe costs \(x\) cents per foot in \(8\)-foot lengths, and \(x + y\) cents per foot in shorter lengths. What is the lowest possible price, in cents, of \(51\) feet of pipe in terms of \(x\) and \(y?\)

A. \(51(x + y)\)
B. \(51x\)
C. \(48x + 3y\)
D. \(48(x + y)\)
E. \(51x + 3y\)

Answer: E

Solution:

For 51 feet of pipe, the cheapest option is to buy six 8-foot pipes and one 3-foot pipe. Therefore, the lowest possible price, in cents, of 51 feet of pipe, is:

6 * 8 * x + 1 * 3 * (x + y) = 48x + 3x + 3y = 51x + 3y

Answer: E