- Submitted By: Tatiyana-Young
- Date Submitted: 12/07/2014 10:29 AM
- Category: Miscellaneous
- Words: 710
- Page: 3

Tatiyana Young

November 8, 2014

18596333

Module 2 Algebraic Equations and Inequalities

Exercise 2.1

Math Problems

1. If 5 times the value of a number is increased by 3, the result is 28. What is the number?

5x+3=28

5x=25

X=5

2. If 4 times the reciprocal of a number is 3 more than 5/2 times the reciprocal of that number, find the number.

4×1/3=3+(5/2)×(1/x)

4/x=3+5/2x

4/x=(6x+5)/2

8=6x+5

6x=3

X=1/2

3. John had $30,000 to invest. He invested part of this money in bonds paying 12% annual simple interest and the rest of the money in a savings account giving 4% annual interest. At the end of the year, he received $2,400 as extra income. How much money did John place in each investment?

.4x+.12(30000-x)=2400

.04x+.12(30000)-.12x=2400

.04x+3600-.12x=2400

.12x-.04x+3600=2400

.08x+3600=2400

.08x+3600-3600=2400-3600

8x=1200

(8x/8)=1200/8

X=1500

15000-30000=15000

Total invested at .12=$15,000.00

At .04=$15,000.00

15000*.04=$600.00

15000*.12=$1,800.00

$1,800.00+$600.00=$2,400.00

4. The length of a football field is 180 feet more than its width. If the perimeter of the field is 1,060 feet, find the length of the field.

L = W + 180

2L + 2W = 1060

substitute:

2(W + 180) + 2W = 1060

2W + 360 + 2W = 1060

4W = 700

W = 175ft

L = 175 + 180 = 355ft

check:

2(355) + 2(175) = 1060

710 + 350 = 1060 checks

The field is 355 feet long.

5. At a school choir concert, 256 students are standing in rows. If the number of students in each row is equal to the total number of rows, find the number of students in each row.

=

= 16

So, the total number of students in each row is 16

6. If 6 times a number is decreased by 8, the result is 40. What is the number?

6x - 8 = 40

6x = 48

x = 8

7. Merry had $20,000 to invest. She invested part of this money in bonds paying 10% annual simple...