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Algebra Worksheets - Page 3

Algebra Worksheets
  • Page 3
 21.  
Express the equation 10 - 8b = 6a - 2a - 6 so that a is a function of b.
a.
a = - 2b + 4
b.
a = - 8b
c.
a = 2b - 16
d.
a = 2 - 16b


Solution:

10 - 8b = 6a - 2a - 6
[Original equation.]

10 - 8b = 4a - 6
[Combine like terms.]

16 - 8b = 4a
[Add 6 on both sides.]

(16 - 8b4) = a
[Divide each side by 4.]

So, a = - 2b + 4


Correct answer : (1)
 22.  
Solve the equation for u, 3u + 6v = - 3u - 6v.
a.
u = 12y
b.
u = - 12v - 6
c.
u = - 6v
d.
u = (- 2 )v


Solution:

3u + 6v = - 3u - 6v
[Original equation.]

3u + 3u = - 6v - 6v
[Add 3u to both sides and then subtract 6v from both sides.]

6u = - 12v

u = ( - 126)v
[Divide each side by 6.]

u = - 2 v


Correct answer : (4)
 23.  
Express the equation - 7(8a - 7b) = 56 + 15a so that a is a function of b.
a.
a = 49b71
b.
a = 127 - 49b
c.
a = (- 56 + 49b)71
d.
a = - 15 - 49b


Solution:

- 7(8a - 7b) = 56 + 15a
[Original equation.]

- 56a + 49b = 56 + 15a

- 56a - 15a + 49b = 56
[Subtract 15a from each side.]

- 71a = 56 - 49b
[Subtract 49b from each side.]

a = (56 - 49b)- 71

a = (- 56 + 49b)71


Correct answer : (3)
 24.  
Use the equation y = (- 10z - 10)9 to find the value of y for z = - 2, - 1, 0, 1
a.
y = - 109, 0, - 109, - 20 9
b.
y = - 109, 0, 0, - 20 9
c.
y = 109 , 0, - 109 , - 20 9
d.
y = - 109, 0, 109, - 20 9


Solution:

y = (- 10z - 10)9
[Given equation.]

y = (- 10(- 2) - 10)9 = 10 / 9
[Substitute z = - 2}.]

y = (- 10(- 1) - 10)9 = 0
[Substitute z = - 1.]

y = (- 10(0) - 10)9 = - 10 / 9
[Substitute z = 0.]

y = (- 10(1) - 10)9 = - 20 / 9
[Substitute z = 1.]

So, y = 10 / 9, 0, - 10 / 9, - 20 / 9 when z = - 2, - 1, 0, 1


Correct answer : (3)
 25.  
Use the equation y = - 76x + 12 to find the value of y for x = - 2, - 1, 0, 1.
a.
y = - 43 3, - 796, - 12, - 656
b.
y = 43 3, - 796, - 12, 656
c.
y = 43 3, 796, 12, 656
d.
y = - 43 3, - 796, 12, - 656


Solution:

y = - 76x + 12
[Original equation.]

y = - 76 (- 2) + 12 = 43 / 3
[Substitute x = - 2.]

y = - 76 (- 1) + 12 = 796
[Substitute x = - 1.]

y = - 76 (0) + 12 = 12
[Substitute x = 0.]

y = - 76 (1) + 12 = 656
[Substitute x = 1.]

So, y = 43 / 3, 796 , 12, 656 when x = - 2, - 1, 0, 1.


Correct answer : (3)
 26.  
Rewrite the equation, 9u - 3(v - 3) = 22 + v, so that v is a function of u.
a.
v = 3u - 94
b.
v = 9u - 134
c.
v = 3u - 13
d.
v = 9u - 35


Solution:

9u - 3(v - 3) = 22 + v
[Original equation.]

9u - 3v + 9 = 22 + v

9u = 13 + 4v
[Add 3v to both sides and then subtract 9 from both sides.]

9u - 13 = 4v
[Subtract 13 form each side.]

9u - 134 = v
[Divide each side by 4.]

v = 9u - 134


Correct answer : (2)
 27.  
Rewrite the equation so that k is a function of l.
10l - 15(5l - 10k) = 12(k - 1) + 6
a.
k = 65l - 11138
b.
k = 65l-6138
c.
k = (65l + 6)
d.
k = 65l+6138


Solution:

10l - 15(5l - 10k) = 12(k - 1) + 6
[Original equation.]

10l - 75l + 150k = 12k - 12 + 6

- 65l + 150k = 12k - 6
[Combine like terms.]

138k = 65l - 6
[Add 65l to both sides and then subtract 12k from both sides.]

(138138)k = 65l - 6138
[Divide each side by 138.]

k = (65l - 6)138


Correct answer : (2)
 28.  
Convert 20°C into Fahrenheit scale by using the formula, F = (9 5)C + 32.
a.
64°F
b.
68°F
c.
72°F
d.
75°F


Solution:

F = 95C + 32
[Original formula.]

F = (95) × 20 + 32
[Replace C with 20.]

= (9)(4) + 32
[Divide.]

= 36 + 32
[Multiply.]

= 68
[Simplify.]

20°C is equal to 68°F.


Correct answer : (2)
 29.  
The L.C.M and G.C.F of two numbers are 150 and 5. If one of the numbers is 25, then find the other number.
a.
36
b.
30
c.
25
d.
35


Solution:

Let n be the unknown number.

The product of two numbers = Product of their L.C.M and G.C.F.
[Formula.]

n × 25 = 150 × 5
[Substitute the values.]

25n25 = 150 × 525
[Divide each side by 25.]

n = 30
[Simplify.]

So, the other number is 30.


Correct answer : (2)
 30.  
An airplane flew 1452 miles at an average speed of 363 miles/hour. How long does it take to fly the entire distance?
a.
7 hours
b.
5 hours
c.
6 hours
d.
4 hours


Solution:

An airplane flew 1452 miles at an average speed of 363 miles/hour.

Time = DistanceSpeed
[Formula.]

Time = 1452363
[Substitute.]

= 4
[Simplify.]

The airplane took 4 hours to travel 1452 miles.


Correct answer : (4)

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