Algebra and equations-help please

Question

1. If a=4, b=6 and d=5, work out the values of these formulas.

a) 3d-5a    b) 2b/7    c) ab/2+d   d) b(2d-a)

2. Work out the values of n in these equations

a) n-4=11      b) 3n=25      c) n/6=3     d) 3n+7=12    e) 4(n-7)   f) 3n/4=-5 

g) 3n/2+4=9

3. Expand the brackets and simplify.

a) 4(n-7)      b)  3(5n+2)     c)   4(n-9)+7    d)  2(5n-3+4n

4. Expand the brackets, simplify then find the value of n in each equation.

a) 4(n-3)=10   b) 3(2n+5)=10   c) 5(n-2)+3=8   d) 5(n-3)+2n=13   e) 2(4n-5)-10=0

5. Find the unknown amount in the following formulas.

a) D= M/V      D=32,M=12, find V

b) V=π×r^2×h=πr^2h 

(i) V=169.56, π=3.14, r=3 Find h

(ii) V=226.08, π=3.14, h=8 Find r

c) R=√2D/5  R=3 Find D

d) W=1.4A-0.5T

(i) W=4.4, T=8 Find A

(ii) W=2, A=5 Find T

6. Find the unknown amounts in the following.

a) 2/3 of U=24   b) 20% of P=8   c) 2/5 of T=9  d) 70% of W=21

Answer 1

1) a = 4,b = 6,d = 5

Substitute the values of a,b,d in given expressions

a) 3d-5a = 3(5)-5(4) = 15-20 = -5

b) 2b/7 = (2*6)/7 = 12/7

c) ab/2+d = (4)(6)/2+5 = 24/7

d) b(2d-a) = 6((2*5)-4) = 6(10-4) = 36

2) a) n-4 = 11

Add 4 to each side.

n-4+4 = 11+4

n = 15

b) 3n = 25

Divide to each side by 3.

3n/3 = 25/3

n = 25/3

c) n/6 = 3

Multiple to each side by 6.

n/6*6 = 3*6

n = 18

d) 3n+7 = 12

Subtract 7 from each side.

3n+7-7 = 12-7

3n = 5

Divide to each side by 3.

3n/3 = 5/3

n = 5/3

f) 3n/4 = -5

Multiple to each side by 4.

3n/4*4 = -5*4

3n = -20

Divide to each side by 3.

3n/3 = -20/3

n = -20/3

g) 3n/2+4 = 9

3n/6 = 9

Multiple to each side by 6.

3n/6*6 = 9*6

3n = 54

Divide to each side by 3.

3n/3 = 54/3

n = 54/3

n = 18

3)a) 4(n-7)

By distributive law.

4n-28

b) 3(5n+2)

15n+6

c) 4(n-9)+7

4n-36+7

4n-29

d) 2(5n-3+4n)

10n-6+8n

2n-6

Answer 2

4)a) 4(n-3)=10

Divide to each side by 4.

4/4(n-3) = 10/4

n-3 = 10/4

Add 3 to each side.

n-3+3 = 10/4+3

n = (10+12)/4

n = 22/4

b) 3(2n+5)=10

Multiple to each side by3.

3/3(2n+5) = 10/3

2n+5 = 10/3

Subtract 5 from each side.

2n+5-5 = 10/3-5

2n = (10-15)3

2n = -5/3

Divide to each side by 2.

2n/2 = -5/3/2

n = -5/6

c) 5(n-2)+3=8

Subtract 3 from each side.

5(n-2)+3-3 = 8-3

5(n-2) = 5

Divide to each side by 5.

5(n-2)/5 = 5/5

n-2 = 1

Add 2 to each side.

n-2+2 = 1+2

n = 3

d) 5(n-3)+2n=13

5n-15+2n = 13

7n-15 = 13

Add 15 to each side.

7n-15+15 = 13+15

7n = 28

Divide to each side by 7.

7n/7 = 28/7

n = 4

e)2(4n-5)-10=0

8n-10-10 = 0

8n-20 = 0

Add 20 to each side.

8n-20+20 = 0+20

8n = 20

Divide to each side by 8.

8n/8 = 20/8

n = 20/8

Answer 3

5) Substitute given values in the formulae to find unknown variable.

a) D = M/V      

D = 32, M = 12

32 = 12/v

Cross multiplication.

32v = 12

Divide to each side by 32.

32v/32 = 12/32

⇒ v = 3/8

b) V = π×r^2×h = πr^2h

(i) V = 169.56, π = 3.14,r = 3

169.56 = 3.14*3*3*h

Divide to each side by 3.14*3*3.

169.56/3.14*3*3 = 3.14*3*3*h/3.14*3*3

⇒ h = 6

(ii) V = 226.08, π = 3.14, h = 8

226.08 = 3.14*r^2*8

Divide to each side by 3.14*8

226.08/3.14*8 = 3.14*8*r^2/3.14*8

9 = r^2

r = sqrt(9)

⇒ r = 3

c) R = √2D/5  

R = 3

3 = √2D/5

Multiple to each side by 5.

3*5 = √2D*5/5

15 = √2D

Dvide to each side by √2.

15/√2 =√2 D/√2

⇒ D = 10.60

d) W = 1.4A-0.5T

(i) W = 4.4, T = 8

4.4 = 1.4A - 0.5*8

4.4 = 1.4A-4

Add 4 to each side.

4.4+4 = 1.4A-4+4

8.4 = 1.4A

Dvide to each side by 1.4

8.4/1.4 = 1.4A/1.4

⇒ A = 6

(ii) W = 2, A = 5

2 = 1.4*5+0.5T

2 = 7+0.5T

Subtract 7 from each side.

2-7 = 7-7+0.5T

-5 = 0.5T

Dvide to each side by 0.5.

-5/0.5 = 0.5T/0.5

-10 = T

⇒ T = -10

 

Answer 4

6)a) 2/3 of U = 24

2/3*U = 24

Multiple to each side by 3/2.

(2/3*3/2)U = 24*3/2

⇒ U = 36

b)20% of p = 8

20/100*p = 8

1/5*p = 8

Multiple to each side by 5.

5/5*p = 8*5

⇒ p = 40

c)2/5 of T = 9

2/5*T = 9

Multiple to each side by 5/2

2/5*5/2 *T = 9*5/2

⇒ T = 45/2

d)70% of W = 21

70/100*W = 21

7/10*W = 21

Multiple to each side by 10/7.

7/10*10/7*W = 21*10/7

⇒ W = 30