Problem 1 :
If (x/2) + 3 = (3/4) - x, what is the value of x ?
(A) 4/5 (B) -3/2 (C) 3/2 (D) 1/5
Problem 2 :
There are one hundred forty-two students in a high school band. These Students represent two ninth of the total students in the high school. How many students attend the school ?
(A) 587 (B) 613 (C) 639 (D) 665
Problem 3 :
If
x-(3-2x)+(4-5x) = -7
what is the value of x ?
(A) 4 (B) 5 (C) -7 (D) 2
Problem 4 :
If three quarters of a number decreased by twenty is equal to eighty two. What is that number ?
(A) 100 (B) 136 (C) 96 (D) 90
Problem 5 :
Which group of algebraic expressions represents three consecutive Integers ?
(A) n, n+2, n+4 (B) n, n+1, n+3
(C) n, n+1, n+2 (D) n, n+3, n+4
Problem 6 :
Julie has twice as many nickels as pennies. She has 120 coins altogether. Which equation represents this situation ?
(A) x.2x = 120 (B) 2x = 120
(C) x+5x = 120 (D) x+2x = 120
Problem 7 :
A pen cost 55 cents more than a pencil. Together they cost 95 cents. How much does the pencil cost ?
(A) $40 (B) $1.50 (C) $20 (D) $75
Problem 8 :
The sum of Joe and Luis’ ages is 22. Joe is two years older than Luis. How old is Joe ?
(A) 22 (B) 20 (C) 10 (D) 12
Problem 9 :
Ruth earned 10 points more than Sara. Together they earned 54 points. How many points did each girl earn ?
(A) 22 and 32 points (B) 54 and 10 points
(C) 20 and 34 points (D) Both are same points
Problem 10 :
Elliot is 3 years older than Charlie. The sum of their ages is 13. How old is each boy ?
(A) Age 13 and 3 (B) Age 5 and 8
(C) Age 10 and 3 (D) Both are same
Problem 11 :
Together Jon and Miriam earned $150. Miriam earned twice as much as Jon. How much did each earn ?
(A) 50 and 100 dollars (B) 70 and 80 dollars
(C) 150 and 20 dollars (D) Both are same
Problem 12 :
Phil worked 5 days more than Jill. Together they worked 25 days. How many days did each work ?
(A) 20 and 5 days (B) 25 and 10 days
(C) 10 and 15 days (D) Both are same
Problem 13 :
Find three consecutive integers whose sum is 72.
(A) 23, 22, 21 (B) 23, 24, 25
(C) 26, 28, 29 (D) 21, 25, 27
Problem 14 :
Find four consecutive integers whose sum is -74.
(A) 17, 18, 19, 20 (B) 20, 19, 18, 17
(D) -17, -18, -19, -20 (D) -20, -19, -18, -17
1. Answer :
(x/2)+3 = (3/4)-x
x/2 + x = (3/4) - 3
3x/2 = (3-12)/4
3x/2 = -9/4
x = -(9/4) ⋅ (2/3)
x = -3/2
So, the value of x is -3/2.
2. Answer :
Let x be the total number of students.
Number of students in the band = 142 students.
2/9 of x = 142
(2/9) ⋅ x = 142
x = 142 ⋅ (9/2)
x = 639
Therefore, 639 students attend the school.
3. Answer :
x-(3-2x)+(4-5x) = -7
x-3+2x+4-5x = -7
x+2x-5x-3+4 = -7
3x-5x+1 = -7
-2x = -7-1
-2x = -8
x = 8/2
x = 4
So, the value of x is 4.
4. Answer :
Let x be the unknown.
3/4 of x-20 = 82
3x/4 = 82+20
3x/4 = 102
x = 102 ⋅ (4/3)
x = 34×4
x = 136
So, the required number is 136.
5. Answer :
Let n be the integers.
Then, the first three consecutive integers is,
n, n+1, n+2.
6. Answer :
Let x be the pennies and nickels 2x.
Given, x+2x = 120
So, x+2x = 120.
So, Option (D) is the answer.
7. Answer :
Let cost of a pencil be x.
Cost of pen = x+55.
Given, x+x+55 = 95
2x+55 = 95
2x = 40
x = 20
So, The cost of pencil $20.
8. Answer :
Let Luis's age = x.
Joe's age = x+2.
Given, x+x+2 = 22
2x+2 = 22
2x = 20
x = 10
So, Luis age is 10.
Joe age is 10+2 = 12.
Therefore, Joe age is 12.
9. Answer :
Let, Sara earn = x points.
Ruth earn = x+10 points.
Given, x+x+10 = 54
2x+10 = 54
2x = 44
x = 22
So, Sara earned 22 points.
Ruth earned 22+10 = 32 points.
Therefore, Each girl earned 22 and 32 points.
10. Answer :
Let, Charlie age = x.
Elliot age = x+3.
Given, x+x+3 = 13
2x = 10
x = 5
So, Charlie age is 5.
Elliot age is 5+3 = 8.
Therefore, Each boy age is 5 and 8.
11. Answer :
Let, Jon earn = x dollars.
Miriam earn = 2x dollars.
Given, x+2x = 150
3x = 150
x = 150/3
x = 50
So, Jon earned 50 dollars.
Miriam earned 2(50) = 100 dollars.
Therefore, Each earned 50 and 100 dollars.
12. Answer :
Let, Jill work = x days.
Phil work = x+5 days.
Given, x+x+5 = 25
2x = 25-5
2x = 20
x = 10
So, Jill work 10 days.
Phil work 10+5 = 15 days.
Therefore, Each work 10 and 15 days.
13. Answer :
Let, first three consecutive integers is n, n+1, n+2
Given, Sum of three consecutive integers is 72
Then, n+n+1+n+2 = 72
3n+3 = 72
3n = 69
n = 23
So, n, n+1, n+2
23, 23+1, 23+2
23, 24, 25
Therefore, Three consecutive integers are 23, 24, 25.
14. Answer :
Let, four consecutive integers is n, n+1, n+2, n+3
Given, Sum of four consecutive integers is -74
Then, n+n+1+n+2+n+3 = -74
4n+6 = -74
4n = -74-6
n = -80/4
n = -20
Therefore, the four consecutive integers are
-20, -19, -18, -17
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Oct 04, 22 11:07 PM
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