Date: 8/22/96 at 9:17:24 From: Anonymous Subject: Stickers Jack and Paul together have 270 stickers. Jack will have twice as many stickers as Paul if Paul gives him 18 stickers. a) Find the number of stickers Paul starts with. b) How many more stickers does Jack have than Paul at the beginning?
Date: 8/30/96 at 14:38:32 From: Doctor Jerry Subject: Re: Stickers Let J be the number of stickers Jack has at the beginning and P be the number of stickers Paul has at the beginning. The first sentence says that J + P = 270. The second sentence is trickier and you should read it very, very carefully. After Paul gives Jack 18 stickers, Paul will have P-18 stickers and Jack will have J + 18. We are told that J + 18 =2 (P - 18). So, we have the two equations J + P = 270 J + 18 = 2P - 36. If you subtract these equations, the J will go away. The result is P - 18 = 270 - (2P - 36) = 270 - 2P + 36. Take the -2P to the left and the -18 to the right. This gives 3P = 270 + 36 + 18 3P = 324 P = 108. Since J + P = 270, J = 270 - 108 = 162. So, the answer to a) is 108 and the answer to b) is J - P = 162 - 108 = 54. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.