﻿ Algebra Worksheets - Page 2 | Problems & Solutions

# Algebra Worksheets - Page 2

Algebra Worksheets
• Page 2
11.
The total surface area of a cuboid is given by the formula A = 2($\mathrm{lw}$ + $\mathrm{wh}$ + $\mathrm{lh}$). 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.

12.
The sum of $n$ terms of an Arithmetic Progression, ${S}_{n}$, is given by the formula ${S}_{n}$ = $\frac{n}{2}$($a$ + $l$), 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.

13.
Find the celsius temperature that corresponds to a room temperature of 50oF by using the formula F = $\frac{9}{5}$C + 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.

14.
Rewrite the equation - 3$r$ + $s$ = 5$s$ so that $s$ is a function of $r$.
 a. $s$ = - 3$r$ - 4 b. $s$ = - $\frac{1}{3}r$ c. $s$ = $\frac{3}{4}r$ d. $s$ = - $\frac{3}{4}r$

#### Solution:

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

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

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

s = - 34r

15.
Rewrite the equation - 48$k$ + 7$l$ = 8$k$ - 49 so that $l$ is a function of $k$.

#### Solution:

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

7l = 8k + 48k - 49

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

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

l = 8k - 7

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

17.
Rewrite the equation 3($c$ - 5$d$) = - 15 ($c$ + 5$d$) so that $d$ is a function of $c$.
 a. $d$ = - 18$c$ - 60 b. $d$ = - 18$c$ + 60 c. $d$ = $\frac{1}{3}$$c$ d. $d$ = - $\frac{3}{10}$$c$

#### 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

18.
Rewrite the equation - 6$x$ + 2$y$ = 6$x$ - 4$y$ - 12 so that $y$ is a function of $x$.
 a. $y$ = 12$x$ - 12 b. $y$ = 2$x$ - 2 c. $y$ = 6$x$ - 4 d. $y$ = 6$x$ - 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

19.
Solve the equation for $c$.
8$c$ + $d$ = 40
 a. $c$ = $d$ - 8 b. $c$ = 5$d$ - 8 c. $c$ = 5 - $\frac{d}{8}$ 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

20.
Express the equation 20$b$ - 4($a$ - 9) = 41 so that $a$ is a function of $b$.
 a. $a$ = - $\frac{5}{4}$ + 5$b$ b. $a$ = 5 + 5$b$ c. $a$ = 10 + 20$b$ d. $a$ = $\frac{5}{4}$ - $b$

#### 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