WRITING EQUATIONS AND SOLVING WORKSHEET

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

Answers

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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