Length and Savings Account
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 The answer is 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/x)=(5/2)*(1/x)+3
4/x=(5/2x)+3
(8/2x)=(5/2x)+3
(8/2x)-(5/2x)=3
(3/2x)=3
x=1/2
The answer would be 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
John put 2400 in each investment.
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 x= length y= width x=y+180 2x+2y=1060 x-y=180 2x+2y=1060
2(y+180)+2y=1060
2y+360+2y=1060
4y+360-360=1060-360
y=175 x=y+180 x=175+180 x=355 The length of the field is 355ft, and the width of the field is 175.
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.
6.
16*16=256
The answer would be 16
7. If 6 times a number is decreased by 8, the result is 40. What is the number?
8. 6x-8=40
6x=40
x=8
The answer would be 8
9. Merry had $20,000 to invest. She invested part of this money in bonds paying 10% annual simple interest and the rest of the money in a savings account giving 5% annual interest. At the end of the year, she received $1,800 as extra income. How much money did merry place in the
5x+3=28
5x=25 x=5 The answer is 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/x)=(5/2)*(1/x)+3
4/x=(5/2x)+3
(8/2x)=(5/2x)+3
(8/2x)-(5/2x)=3
(3/2x)=3
x=1/2
The answer would be 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
John put 2400 in each investment.
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 x= length y= width x=y+180 2x+2y=1060 x-y=180 2x+2y=1060
2(y+180)+2y=1060
2y+360+2y=1060
4y+360-360=1060-360
y=175 x=y+180 x=175+180 x=355 The length of the field is 355ft, and the width of the field is 175.
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.
6.
16*16=256
The answer would be 16
7. If 6 times a number is decreased by 8, the result is 40. What is the number?
8. 6x-8=40
6x=40
x=8
The answer would be 8
9. Merry had $20,000 to invest. She invested part of this money in bonds paying 10% annual simple interest and the rest of the money in a savings account giving 5% annual interest. At the end of the year, she received $1,800 as extra income. How much money did merry place in the