Math Word Problems Demystified - A Self Teaching Guide

EXAMPLE:Find the solution to 2xþx^2 ¼8. SOLUTION: Step 1: Write the equation in standard form x^2 þ 2 x
8 ¼ 0 Step 2: Factor th ...

SOLUTION: Step 1: Write in standard form 2 x^2
3 x
5 ¼ 0 Step 2: Factor the left member ð 2 x
5 Þðxþ 1 Þ¼ 0 Step 3: Set both ...

Step 4: Solve each equation x
3 þ 3 ¼ 0 þ 3 xþ 3
3 ¼ 0
3 x¼ 3 x¼
3 EXAMPLE:Solvex^2 ¼ 6 x. SOLUTION: Step 1: x^2
6 x¼ 0 ...

SOLUTIONS: 1 : x^2
9 x¼
18 x^2
9 xþ 18 ¼ 0 ðx
3 Þðx
6 Þ¼ 0 x
3 ¼ 0 x
6 ¼ 0 x
3 þ 3 ¼ 0 þ 3 x
6 þ 6 ¼ 0 þ 6 x¼ 3 x¼ 6 ...

4 : 6 x^2
11 x¼ 10 6 x^2
11 x
10 ¼ 0 ð 2 x
5 Þð 3 xþ 2 Þ¼ 0 2 x
5 ¼ 03 xþ 2 ¼ 0 2 x
5 þ 5 ¼ 0 þ 53 xþ 2
2 ¼ 0
2 2 x¼ ...

19 LESSON Solving Word Problems Using REFRESHER VI Quadratic Equations Many problems in mathematics can be solved using a quadra ...

meaningful. This will be shown in some problems. In that case, disregard the solution that does not make sense. (Note:Sometimes ...

SOLUTION: GOAL: You are being asked to find two consecutive numbers whose product is 306. STRATEGY: Letx¼the first number andxþ ...

SOLUTION: GOAL: You are being asked to find two numbers whose sum is 12 and whose reciprocal sum is^38 : STRATEGY: Letx¼one numb ...

EVALUATION: The sum of 4þ 8 ¼12. The sum of the reciprocals is 1 4 þ 1 8 ¼ 2 8 þ 1 8 ¼ 3 8 : Try These The square of a number p ...

Letx¼one number andxþ 6 ¼the other number xðxþ 6 Þ¼ 91 x^2 þ 6 x¼ 91 x^2 þ 6 x
91 ¼ 91
91 x^2 þ 6 x
91 ¼ 0 ðxþ 13 Þðx
7 Þ ...

The answers are
15 and
17, and 15 and 17. Letx¼the smaller number andxþ 3 ¼the larger number x^2 ¼ 3 ðxþ 3 Þþ 19 x^2 ¼ 3 xþ 9 ...

60 xþ 960 ¼x^2 þ 32 x 60 x
60 xþ 960 ¼x^2 þ 32 x
60 x 960 ¼x^2
28 x 960
960 ¼x^2
28 xþ 960 0 ¼x^2
28 xþ 960 0 ¼ðx
48 ...

20 LESSON Solving Word Problems in Geometry Although word problems in geometry are for the most part different from those in alg ...

Geometric principle: The sum of the measures of the angles of a triangle is 1808. SOLUTION: GOAL: You are being asked to find th ...

x¼ 368 2 x¼ 2  368 ¼ 728 Hence the measures of each of the angles are 36 8 ,72 8 , and 72 8. EVALUATION: See if the sum of the ...

IMPLEMENTATION: Solve the equation: 2 ð 4 xÞþð 2 xÞ¼ 80 8 xþ 2 x¼ 80 10 x¼ 80 101 x 101 ¼ 80 10 x¼ 8 4 x¼ 4  8 ¼ 32 Hence the l ...

See Figure 20-3. SinceA¼^12 bh, the equation is 8¼^12 ðxþ 6 Þx: IMPLEMENTATION: Solve the equation: 8 ¼ 1 2 ðxþ 6 Þx 2  8 ¼ 2  ...

EVALUATION: Find the area and see if it is 8 inches. A¼ 1 2 bh ¼ 1 2 ð 8 Þð 2 Þ ¼8 square inches: Try These The perimeter of a ...

The base of a triangle is 7 feet longer than its height. If its area is 30 square feet, find the measures of the base and heigh ...