Ws Algebraicratios Key

Mathletics Fall, 2009

Ratios —

A

Name: Mr. Hershman

Part I. (14 points) Solve without the use of a calculator 1. Give four possible answers to the prompt: state three numbers with a ratio of 4 : 7 : 9 2 pts

2. The sum of three numbers is 100 and the numbers have a ratio of 5 : 7 : 13 What are the three numbers?

2 pts

3. The ratio of the interior angles in a triangle is 5 : 7 : 18 what are the angles? 2 pts

4. The ratio of the interior angles in a quadrilateral is 3 : 1 : 4 : 6 what is the largest angle? 2 pts

5. The ratio of the area of one square to the area of another is side lengths?

16 . 25

What is the ratio of the 2 pts

6. Write a ratio problem involving the interior angles of a pentagon and show the solution 2 pts

7. The ratio of the interior angles of a triangle is 3 : 29 : x. Assuming integral measures, give all possible values of x in the ratio.

2 pts

Mathletics/A Solutions to Ratios —

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SOLUTIONS

A

1. 4 : 7 : 9 and 8 : 14 : 18 and 12 : 21 : 27  2. 20 + 28 + 52 = 100  3. 5x + 7x + 18x = 180 30x = 180 x=6 30 : 42 : 108

(1) (2) (3) (4) 

4. 216◦  5.

q

16 25

=

4 5

 6. The sum of the interior angles of a polygon is 180(n − 2) where n is the number of sides. So the sum of the interior angles should be 540◦ . Problems will vary.  7. 180 − 3v + 29v = x so for the following values of v 1148 2116 384 452 520

(5) (6) (7) (8) (9)

The possible values of x in the ratio are 148, 116, 84, 52, and 20.