Practice with Literal Equations Topic Index | Algebra Index | Regents Exam Prep Center

Solve for the indicated variable in questions 1 - 5:

 1.  Solve for  p: Answer Multiply both sides by the reciprocal of 1/3 which is 3/1. The answer is p = 3n. 2.  Solve for  y: xy - d = m Answer Add d to both sides to get xy = m + d. Now, divide both sides by x to get the answer y = (m+d)/x. 3.  Solve for  y: Answer Subtract c from both sides to get (y/2) = d - c. Multiply both sides by the reciiprocal of 1/2 which is (2/1). (2/1)(y/2) = (2/1)(d - c) y = 2(d - c) y = 2d - 2c 4.  Solve for  w: V = l w h Answer Divide both sides by l times h. V/lh = w 5.  Solve for  w: P = 2l + 2w Answer Subtract 2l from both sides to get P - 2l = 2w Divide both sides by 2. (P - 2l)/2 = w

6.  Lightning quickly heats the air causing it to expand, which produces the sound of thunder.  Sound travels approximately 1 mile in 5 seconds.  Knowing  D = rt,  how far away is a thunderstorm when you notice a 3-second delay between the flash of lightning and the sound of thunder?   (D = distance, r = rate, t = time)

 Answer Solve D = rt for the variable r. Divide both sides by t to get D/t = r. D = 1 mile. t = 5 seconds r = 1/5 mile per second 3-second delay means 3 (1/5) = 3/5 Answer: 3/5 mile away.

 7 Your school is ordering computer equipment.  Let c represent the cost of one personal computer and p represent the cost of one printer.

a.  Write an expression for the total cost of 15 personal computers and 8 printers.

 Answer 15c + 8p

b. The school discovers that it needs 8 additional computers and 4 additional printers. Write an expression for the total cost of this additional equipment.

 Answer 8c + 4p

c. Write an expression that will represent the total amount of money spent on computer equipment.

 Answer 23c + 12p

 8 Bryan and Nate are dirt bike racers and are brothers.  Bryan gives his younger brother, Nate, a 60 meter head start during a practice run.

After t seconds, Nate is a distance 6t + 60 from the starting line and Bryan is a distance of 7t from the starting line.

a.  How far ahead of Bryan is Nate after t seconds?

 Answer -t + 60 meters. (Nate's position subtract Bryan's position: 6t+60 - 7t)

b.  Evaluate the answer for part  a  when:

 1.) t = 15 Answer 45 m (Solve -15 + 60) 2.) t = 30 Answer 30 m (solve -30 + 60) 3.) t = 45 Answer 15 m (Solve -45 + 60)

c.  Does Bryan ever catch up with Nate?  If so, after how many seconds?

 Answer Yes, after 60 sec. This is when -t + 60 = 0.

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