﻿ Algebra Worksheets - Page 3 | Problems & Solutions

# Algebra Worksheets - Page 3

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

#### Solution:

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

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

16 - 8b = 4a

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

So, a = - 2b + 4

22.
Solve the equation for $u$, 3$u$ + 6$v$ = - 3$u$ - 6$v$.
 a. $u$ = 12$y$ b. $u$ = - 12$v$ - 6 c. $u$ = - 6$v$ 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

23.
Express the equation - 7(8$a$ - 7$b$) = 56 + 15$a$ so that $a$ is a function of $b$.
 a. $a$ = $\frac{49b}{71}$ b. $a$ = 127 - 49$b$ c. $a$ = d. $a$ = - 15 - 49$b$

#### 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

24.
Use the equation $y$ = to find the value of $y$ for $z$ = - 2, - 1, 0, 1
 a. $y$ = - $\frac{10}{9}$, 0, - $\frac{10}{9}$, - $\frac{20}{9}$ b. $y$ = - $\frac{10}{9}$, 0, 0, - $\frac{20}{9}$ c. $y$ = $\frac{10}{9}$ , 0, - $\frac{10}{9}$ , - $\frac{20}{9}$ d. $y$ = - $\frac{10}{9}$, 0, $\frac{10}{9}$, - $\frac{20}{9}$

#### 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

25.
Use the equation $y$ = - $\frac{7}{6}$$x$ + 12 to find the value of $y$ for $x$ = - 2, - 1, 0, 1.
 a. $y$ = - $\frac{43}{3}$, - $\frac{79}{6}$, - 12, - $\frac{65}{6}$ b. $y$ = $\frac{43}{3}$, - $\frac{79}{6}$, - 12, $\frac{65}{6}$ c. $y$ = $\frac{43}{3}$, $\frac{79}{6}$, 12, $\frac{65}{6}$ d. $y$ = - $\frac{43}{3}$, - $\frac{79}{6}$, 12, - $\frac{65}{6}$

#### 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.

26.
Rewrite the equation, 9$u$ - 3($v$ - 3) = 22 + $v$, so that $v$ is a function of $u$.
 a. $v$ = b. $v$ = c. $v$ = 3$u$ - 13 d. $v$ = 9$u$ - 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

27.
Rewrite the equation so that $k$ is a function of $l$.
10$l$ - 15(5$l$ - 10$k$) = 12($k$ - 1) + 6
 a. $k$ = b. $k$ = $\frac{65l-6}{138}$ c. $k$ = (65$l$ + 6) d. $k$ = $\frac{65l+6}{138}$

#### 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

28.
Convert 20°C into Fahrenheit scale by using the formula, F = ($\frac{9}{5}$)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.

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.

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.