Question 1

Given the formula $$P = 2QR + 2QS$$, solve for $$Q in $$terms of $$P$$, $$R$$, and $$S.$$

Accepted Answer

$$Q = \dfrac{P}{2(R+S)}$$

Question 2

A manufacturer uses the formula $$P = 2QR + 2QS to $$calculate the perimeter $$P of a $$rectangular frame, where $$Q is $$the number of frames, $$R is $$the length, and $$S is $$the width. If the total perimeter needed is $$P = 400$$ units, $$R = 5$$ units, and $$S = 3$$ units, how many frames $$Q$$ can be made?

Accepted Answer

$$Q = 50$$

Question 3

If $$P = 2QR + 2QS$$ and $$Q = 10$$, $$R = 4$$, $$S = 6$$, what is the value of $$P$$?

Accepted Answer

$$P = 200$$

Question 4

Which of the following correctly isolates $$Q in $$the equation $$P = 2QR + 2QS$$?

Accepted Answer

$$Q = \dfrac{P}{2(R+S)}$$

Question 5

A company wants to maximize the number of products $$Q it $$can produce given a fixed perimeter $$P$$ using the formula $$P = 2QR + 2QS. If$$ $$R$$ and $$S$$ are both doubled, what happens to the maximum possible $$Q$$?

Accepted Answer

It is halved.

Question 6

Suppose $$P = 2QR + 2QS$$ models the total fencing needed for $$Q$$ identical rectangular gardens, each with length $$R$$ and width $$S. If $$you have 600 meters of fencing and each garden is $$R = 8$$ meters long and $$S = 7$$ meters wide, what is the maximum number of gardens you can build?

Accepted Answer

$$Q = 6$$

Question 7

Given $$P = 2QR + 2QS$$, if $$P = 360$$, $$R = 6$$, and $$S = 9$$, what is the value of $$Q$$?

Accepted Answer

$$Q = 20$$

Question 8

If $$Q = \dfrac{P}{2(R+S)}$$ and $$P = 180$$, $$R = 5$$, $$S = 4$$, what is the value of $$Q$$?

Accepted Answer

$$Q = 20$$

Question 9

A rectangular enclosure is to be built using the formula $$P = 2QR + 2QS. If$$ $$Q = 3$$, $$R = 12$$ meters, and $$S = 8$$ meters, what is the total perimeter $$P$$ required?

Accepted Answer

$$P = 120$$ meters

Question 10

If $$P = 2QR + 2QS$$ and $$Q = 15$$, $$R = 7$$, $$S = 5$$, what is $$P$$?

Accepted Answer

$$P = 360$$

Question 11

A school is building $$Q$$ identical rectangular playgrounds, each with length $$R$$ and width $$S. $$The total fencing available is $$P$$ meters. Which formula gives the maximum number of playgrounds $$Q$$ that can be built?

Accepted Answer

$$Q = \dfrac{P}{2(R+S)}$$

Question 12

If $$P = 2QR + 2QS$$ and $$Q = 8$$, $$R = 10$$, $$S = 5$$, what is $$P$$?

Accepted Answer

$$P = 240$$

Question 13

A company wants to use the formula $$P = 2QR + 2QS to $$determine how many identical rectangular signs ($$Q) $$can be made from a roll of border tape of length $$P. If $$each sign is $$R$$ units long and $$S$$ units wide, which of the following is the correct formula for $$Q$$?

Accepted Answer

$$Q = \dfrac{P}{2(R+S)}$$

Question 14

If $$P = 2QR + 2QS$$ and $$Q = 12$$, $$R = 6$$, $$S = 4$$, what is $$P$$?

Accepted Answer

$$P = 240$$

Question 15

A rectangular garden is to be fenced using the formula $$P = 2QR + 2QS. If$$ $$P = 360$$ meters, $$R = 10$$ meters, and $$S = 8$$ meters, what is the maximum number of gardens $$Q$$ that can be built?

Accepted Answer

$$Q = 20$$

Solving Formulas for a Specified Variable in Precalculus

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