1. If 5 times the value of a number is increased by 3, the result is 28. What is the number?
5x + 3 = 28 -3 -3
5x = 25
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5
X = 5
The number is 5.

2. If 4 times the reciprocal of a number is more than 5/2 times the reciprocal of that number, find the number.
4 (1/x) = 3 + (5/2) (1/x) 4/x = 3 + 5/2x 2x (4/x) = 2x (3+5/2x)
8 = 6x + 5 -5 - 5
3 = 6x
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6
X = ½
The number is ½.

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?
Bonds = x
Savings = 30,000 – x
.12x + .04 (30,000 – x) = 2,400
.12x + 1,200 - .04x = 2,400
.08x + 1,200 = 2,400 -1,200 -1,200
.08x = 1,200
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.08
X = $15,000 (amount put into bonds)
30,000 – 15,000 = $15,000 (amount put into savings)
John put $15,000 into bonds and $15,000 into savings. 4. The length of a football field 180 feet more than its width. If the perimeter of the field is 1,060 feet, find the length of the field.
2w + 2 (180 +w) = 1,060
2w + 360 + 2w = 1,060
4w + 360 = 1,060 -360 -360
4w – 700
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4 w = 175
175 +180 = 355
The length of the field is 355 feet.

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.
256 = x^2
√256 = √x^2
16 = x
X = 16
Each row contains 16 students, and there are 16 rows of students.

6. If 6 times a number is decreased by 8, the result is 40. What is the number?
6x -8 = 40 +8 +8
6x = 48
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6
X = 8
The number is 8.

7. Merry has $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 savings account?
Bonds = x
Savings = 20,000 – x
.1x + .05 (20,000 –x) = 1,800
.1x + 1000 - .05x = 1,800
.15x + 1000 = 1,800 -1000 -1000
.15x = 800
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.15
X = $5,333.33
20,000 – 5,333.33 = 14,666.67
Merry put $5,333.33 into bonds and $14,666.67 into savings.

8. The length of a rectangular field is 50 feet less than its width. If the perimeter of the field is 840 feet, find the length of the field.
2w + 2 (w-50) = 840
2w + 2w – 100 = 840 +100 +100
4w = 940
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4
W = 235
235 – 50 = 185
The length of the field is 185 feet.

9. Alan participated in a car race in which he had to cover a distance of at least 50 kilometers. He had fuel in his car for a maximum distance of 53 kilometers. If the distance is given by S (t)=3t+47, where t is the time in hours, find the minimum and maximum number of hours for which Alan can drive his car.
S (t) = 3t + 47
50 ≤ 3t + 47 ≤ 53
-47 -47 -47
3 ≤ 3t ≤ 6
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3
1 ≤ t ≤ 2
Alan has to drive his car a minimum of 1 hour and a maximum of 2 hours.

10. In a 2-digit number, the number in the unit’s place is 4 more than the number in the tens place. If the digits of the numbers are reversed, the new number is 6 more than thrice the original number. Find the original number.
10x = tens place
X + 4 = units place
10x + x + 4
11x + 4

10 (x + 4) + x = 11x + 40

3 (11x + 4) + 6 = 11x + 40
33x + 12 + 6 = 11x + 40
33x + 18 = 11x + 40
-11x -11x
22x + 18 = 40 -18 -18
22x = 22
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22
X = 1

11 (1) + 4 = 15
The original number is 15.