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...