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Algebra Worksheets - Page 2

Algebra Worksheets
  • Page 2
 11.  
The total surface area of a cuboid is given by the formula A = 2(lw + wh + lh). Find the height of a cuboid whose length is 90 cm, width is 60 cm, and total surface area is 22800 cm2?
a.
45 cm
b.
100 cm
c.
40 cm
d.
130 cm


Solution:

A = 2(lw + lh + wh)

A = 2lw + 2lh + 2wh
[Distributive property.]

A - 2lw = 2lh + 2wh
[Subtract 2lw from both sides.]

A - 2lw = 2h(l + w)
[Distributive property.]

A - 2lw2(l+w) = h
[Divide both sides by 2(l + w).]

The formula is solved for h.

h = A - 2lw2(l+w)

h = 22800-(2×90×60)2(90+60)
[Substitute: A = 22800, l = 90, w = 60.]

h = 22800 - 10800300

h = 12000 / 300 = 40

The height of the cuboid is 40 cm.


Correct answer : (3)
 12.  
The sum of n terms of an Arithmetic Progression, Sn, is given by the formula Sn = n2(a + l), where a is the first term and l is the last term of the A.P. Find the first term of the A.P. if its last term is 10, and the sum of 5 terms is 40.
a.
5
b.
7
c.
6


Solution:

Sn = n2(a + l)

2Snn = a + l

2Snn - l = a
[Solve the formula for a.]

a = 2Snn - l

a = 2 × 405 - 10
[Substitute: Sn = 40, l = 10, n = 5.]

a = 16 - 10 = 6.


Correct answer : (4)
 13.  
Find the celsius temperature that corresponds to a room temperature of 50oF by using the formula F = 9 5C + 32.
a.
6oC
b.
8oC
c.
10oC
d.
4oC


Solution:

F = 95C + 32
[Formula.]

50 = ( 95 ) × C + 32
[Replace the variable with the value, given.]

50 - 32 = ( 95 ) × C + 32 - 32
[Subtract 32 from each side.]

18 = ( 95 ) × C
[Simplify.]

(5)(18) = 5 × ( 95 ) × C
[Multiply by 5 on each side.]

90 = 9C
[Simplify.]

909 = 9C9
[Divide each side by 9.]

10 = C
[Simplify.]

The Celsius temperature corresponding to 50o F is 10oC.


Correct answer : (3)
 14.  
Rewrite the equation - 3r + s = 5s so that s is a function of r.
a.
s = - 3r - 4
b.
s = - 13r
c.
s = 34r
d.
s = - 34r


Solution:

- 3r + s = 5s
[Original equation.]

- 3r = 4s
[Subtract s from each side.]

- (34)r = (44) s
[Divide each side by 4.]

s = - 34r


Correct answer : (4)
 15.  
Rewrite the equation - 48k + 7l = 8k - 49 so that l is a function of k.


Solution:

- 48k + 7l = 8k - 49
[Original equation.]

7l = 8k + 48k - 49
[Add 48k to both sides.]

7l = 56k - 49
[Combine like terms.]

l = 56k - 497
[Divide each side by 7.]

l = 8k - 7


Correct answer : (0)
 16.  
Rewrite the equation 25m + 5(n + 4) = 10 so that n is a function of m.
a.
n = 25m - 10
b.
n = 25m + 5
c.
n = - 5m + 10
d.
n = - 5m - 2


Solution:

25m + 5(n + 4) = 10
[Original equation.]

25m + 5n + 20 = 10
[Evaluate the equation.]

5n = - 25m - 10
[Subtract 25m and 20 from each side.]

n = -25m - 105
[Divide each side by 5.]

n = - 5m - 2


Correct answer : (4)
 17.  
Rewrite the equation 3(c - 5d) = - 15 (c + 5d) so that d is a function of c.
a.
d = - 18c - 60
b.
d = - 18c + 60
c.
d = 1 3c
d.
d = - 3 10c


Solution:

3(c - 5d) = - 15 (c + 5d)
[Original equation.]

3c - 15d = - 15c - 75d
[Evaluate the equation.]

- 15d + 75d = - 15c - 3c
[Add 75d to both sides and then subtract 3c from both sides.]

60d = - 18c

d = - 1860 c
[Divide each side by 60.]

d = - 3 / 10c


Correct answer : (4)
 18.  
Rewrite the equation - 6x + 2y = 6x - 4y - 12 so that y is a function of x.
a.
y = 12x - 12
b.
y = 2x - 2
c.
y = 6x - 4
d.
y = 6x - 12


Solution:

- 6x + 2y = 6x - 4y - 12
[Original equation.]

2y + 4y = 6x + 6x - 12
[Add 4y and 6x to both sides.]

6y = 12x - 12

y = (12x - 12)6
[Divide each side by 6.]

y = 2x - 2


Correct answer : (2)
 19.  
Solve the equation for c.
8c + d = 40
a.
c = d - 8
b.
c = 5d - 8
c.
c = 5 - d8
d.
c = 5 - d


Solution:

8c + d = 40
[Original equation.]

8c = 40 - d
[Subtract d from each side .]

c = (40 - d8)
[Divide each side by 8.]

c = 5 - d8


Correct answer : (3)
 20.  
Express the equation 20b - 4(a - 9) = 41 so that a is a function of b.
a.
a = - 54 + 5b
b.
a = 5 + 5b
c.
a = 10 + 20b
d.
a = 54 - b


Solution:

20b - 4(a - 9) = 41
[Original equation.]

20b - 4a + 36 = 41
[Evaluate equation.]

- 4a = 5 - 20b
[Subtract 20b and 36 from each side.]

a = 5 - 20b- 4
[Divide each side by - 4.]

a = - 54 + 5b


Correct answer : (1)

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