Unit 2: One Variable Equations and Inequalities



Unit 2 : One Variable Equations and Inequalities

Class Notes Day 3- Literal Equations, Applications and Word Problems

I. Introduction

Given a rectangle, the formula for perimeter is .

1) If the perimeter is 68, and the length is 15, find the width. Use the formula above and solve the equation.

II. Literal Equations Examples

1) Solve [pic] for b. 2) Solve [pic] 3) Solve [pic].

4) Solve [pic] 5) Solve[pic] 6) Solve [pic].

7) Solve [pic]. 8) Solve[pic] 7) Solve [pic].

8) Solve [pic] 9) Solve [pic]

III. Practice

I. Solve.

1. A = bh, for b 2. d = rt, for t 3. I = Prt, for P

4. F = ma, for a 5. P = 2l + 2w, for w 6. A = πr2, for π

7. A = [pic]bh, for b 8. E = mc2, for m 9. A = [pic], for b

IV. Application Examples

1) The formula [pic]is often used by placement services to find keyboarding speeds. In the formula, s represents the speed in words per minute, w represents the number of words typed, e represents the number of errors, and m represents the number of minutes typed.

a. Solve the formula for e. b. If Miguel typed 410 words in 5 minutes and received a k

keyboard speed of 76 words per minute, how many

errors did he make?

2) The formula [pic] represents the amount of pressure exerted on the floor by the heel of a shoe. In this formula, P represents the pressure in pounds per square inch, W represents the weight of a person wearing the shoe in pounds, and H is the width of the heel of the shoe in inches.

a. Solve the formula for W. b. Find the weight of the person if the heel is 3 inches wide

and the pressure exerted is 30 pounds per square inch.

V. Geometry Connection: Formulas for Volume

Square Pyramid Formula: [pic] Cylinder Formula: [pic]

Cone Formula: [pic] Sphere Formula: [pic]

Examples:

1) (a) Solve the formula for a cylinder for h. (b) Use this to find the height if the volume is[pic] and

the radius is 4.

2) (a) Solve the formula for a cone for h. (b) Use this to find the height if the volume is [pic] and

the radius is 6.

3) (a) Solve the formula for a square pyramid for h. (b) Use this to find the height is the volume is 400 and

[pic].

4) (a) Solve the formula for a sphere for [pic]. (b) Use this to find [pic] if the volume is [pic].

VI. Basic Word Problems Examples

1) 7 more than a number is 25. Find the

number.

2) 5 less than 2 times Jeff’s age is 43.

Find Jeff’s age.

3) The greater of two numbers is 6 more

than 4 times the smaller. Their sum is 41. Find the numbers.

4) The sum of three numbers is 36. The first is twice the second, while the third is four more than the second. Find the numbers.

VII. Basic Word Problems Practice

1) 8 more than a number is 14. Find the number.

2) Three less than 5 times Wanda’s age is the same as 3 times her age increased by 37. How old is she?

3) The greater of two numbers is 3 more than twice the smaller. Their sum is 24. Find the numbers.

4) The sum of two numbers is 50. The first is 5 less than 4 times the second. Find the numbers.

VIII. Consecutive Integers Examples

1) Find two consecutive integers whose sum is 63.

2) Find three consecutive integers whose sum is 105.

3) Find three consecutive odd integers whose sum is 75.

4) Find three consecutive even integers whose sum is 138.

IX. Consecutive Integers Practice

1) Find two consecutive integers whose sum is 45.

2) Find two consecutive odd integers whose sum is 36.

3) Find four consecutive even integers who sum is 76.

4) Find three consecutive integers such that the sum of the first and the third is 146.

X. Application Examples

1) The length of a rectangle is 5 feet more than twice the width. The perimeter is 70 ft. Find the length and the width.

2) The perimeter of a rectangle is 60. The width is 4 less than the length. Find the length and width

3) One angle of a triangle is 2 times another. The third angle is 10( more than the larger of these. Find the angles.

4) One angle of a triangle is 30( more than another. The third angle is 18( less than the smaller of these. Find the angles

XI. Application Practice

1) The length of a rectangle is 6 feet greater than the width. The perimeter is 40 ft. Find the length and the width.

2) One angle of a triangle is twice as large as another. The third angle contains 5( more than the larger of these. Find each angle.

3) The first side of a triangle is 2 feet longer than the second. The third side is 5 feet shorter than the twice the second. The perimeter is 49 feet. Find the length of each side.

4) The perimeter of a rectangle is 86 inches. If the length is 3 inches longer than the width, find the lengths of each side.

XII. Homework

Define the variables. Write the equation. Solve.

1) The length of a rectangle is 2 feet more than its width. If its perimeter is 40 feet, find the length and the width.

2) One month, John worked 3 hours less than Tia, and Felicia worked 4 hours more than Tia. Together, they worked 196 hours. Find the number of hours each person worked.

3) Find four consecutive even integers whose sum is 100.

4) The sum of two consecutive integers is 57. Find the numbers.

5) In a game, Harry’s score was 3 times Jeff’s score. Together, they scored 32 points. Find their scores.

6) Ten more than a number is –122. Find the number.

7) Twelve less than a number is 114. Find the number.

8) Two-thirds of a number is –12. Find the number.

9) One number is 5 more than 3 times a smaller one. If 4 times the smaller number is subtracted from the larger one, the result is 0. Find the numbers.

10) The sum of three consecutive integers is 105. Find the integers.

11) The sum of three consecutive even integers is 138. Find the integers.

12) The sum of three consecutive odd integers is 285. Find the integers.

13) Rhonda worked three more than twice as many hours as Jim did. Together, they worked 57 hours. How many hours did each of them work?

14) Sam worked five less than twice as many hours as Jane did. How many hours did each work if together they worked 97 hours?

15) The second angle in a triangle is 3( less than twice the first angle. The third angle measure 8( more than twice the first angle. Find each angle.

16) Two of the angles in a triangle have the same measure. The third angle is 15( more than each of the other two. Find the measure of each angle.

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