Problem Solving Worksheets With Answer Key - Math Stars (Page 18 of 39) in pdf

Problem Solving Worksheets With Answer Key - Math Stars Page 18

Vol. 7 No. 5

About these newsletters...

The purpose of the MathStars Newsletters is to challenge students beyond the classroom

setting. Good problems can inspire curiosity about number relationships and geometric

properties. It is hoped that in accepting the challenge of mathematical problem solving,

students, their parents, and their teachers will be led to explore new mathematical hori-

zons.

As with all good problems, the solutions and strategies suggested are merely a sample of

what you and your students may discover. Enjoy!!

Discussion of the problems...

1. Answers will vary. Here are four solutions: 6 x 1 - 2

2; 6 - 1 x 2

2; 6

1- 2

2; 6 x 1

2 + 2.

Students need to be made aware of the application of order of operations in determining correct expres-

sions.

2. [51 and 57] The sum of two consecutive integers will always be odd i.e. x + (x + 1) = 2x + 1. The

sum of three consecutive integers i.e. x + (x + 1) + ( x + 2) = 3x + 3 = 3(x + 1) will be divisible by

three. The only odd integers divisible by three between 50 and 60 are 51 and 57.

3. Answers will vary.

4. [$0.57] Let a = the cost of an apple and b = the cost of a banana. If 2a + 3b = 51, the 4a + 6b = 102.

We are given that 4a + 7b = 111. Comparing the two expressions tells us that one banana costs 9¢.

Using the first equation as a base 2a + 3 x 9 = 51 or 2a = 24. Therefore, an apple costs 12¢. One apple

and five bananas will cost $0.12 + 5 x $0.09 or $0.57.

5. [She should not wait; $34.67 < $39] Today the dress will cost 2/3 of $52 or $34.67. Tomorrow the

dress will cost

1/2 the original price or $39.

6. [83] The process of elimination, as each clue is determined, will yield the solution.

7. [Justin's; $510 < $515] Justin's best price is $200 + $30 + $0.08 x 3500 = $510. At Kelly's the

charges are $140 + $25 + $0.10 x 3500 = $515.

8. [the 11th chair] The first round eliminates those in chairs 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

The second round eliminates those in chairs 1, 5, 9, 13, 17. 21. The third round eliminates those in

chairs 7 and 15. The fourth round eliminates 3 and 19, leaving chair 11 with the grand prize winner!

Problem Solving Worksheets With Answer Key - Math Stars Page 18