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1. Given M = 1/2 × a × b, when M = 65 and a = 10, find b?

## Solution:

Given that M = 1/2 × a × b

To find b, rewrite the given equation by changing the subject to b.

M = 1/2 × a × b

Move 1/2 × a to the left side and divide it with M

2M/a = b

b = 2M/a.

Substitute M = 65 and a = 10 in the above equation.

b = 2(65)/10 = 130/10

b = 13

The final answer is b = 13.

2. Given L = 1/5 n²r when L = 30 and n = 5, find r?

## Solution:

Given that L = 1/5 n²r

To find r, rewrite the given equation by changing the subject to r.

L = 1/5 n²r

Move 1/5 to the left side and multiply it with L.

5L = n²r

Move n² to the left side and divide it with 5L

(5L)/n² = r

r = (5L)/n²

Substitute L = 30 and n = 5 in the above equation.

r = 5 (30)/(5)²

r = 30/5 = 6

r = 6

The final answer is r = 6.

3. Given A = 7b² when A = 700, find b?

## Solution:

Given that A = 7b²

To find b, rewrite the given equation by changing the subject to b.

A = 7b²

Move 7 to the left side and divide it with A

A/7 = b²

Apply square root on both sides.

√(A/7) = √(b²)

√(A/7) = b

b = √(A/7)

Substitute A = 700 in the above equation.

b = √(700/7)

b = √100

b = 10

The final answer is b = 10.

4. Given R = 2 (m + n) when m = 15 and R = 100, find n?

## Solution:

Given that R = 2 (m + n)

To find n, rewrite the given equation by changing the subject to n.

R = 2 (m + n)

Move 2 to the left side and divide it with R

R/2 = m + n

Move m to the left side and subtract it with R/2

R/2 – m = n

n = R/2 – m

Substitute m = 15 and R = 100 in the above equation.

n = R/2 – m

n = (100/2) – 15

n = 50 – 15 = 35

n = 35

The final answer is n = 35

5. Given C = (S × 100)/(100 × g) find S when C= 140 and G = 5?

## Solution:

Given that C = (S × 100)/(100 × g)

To find S, rewrite the given equation by changing the subject to S.

C = (S × 100)/(100 × g)

Move (100 × g) to the left side and multiply it with C

C(100 × g) = S × 100

Move 100 to the left side and divide it with 100

C(100 × g)/100 = S

Cg = S

S = Cg

Substitute C= 140 and G = 5 in the above equation.

S = Cg

S = 140(5)

S = 700

The final answer is S = 700

6. P = Q + R find R if P = 5700 and Q = 2640?

## Solution:

Given that P = Q + R

To find R, rewrite the given equation by changing the subject to R.

P = Q + R

Move Q to the left side and subtract it from the P.

P – Q = R

R = P – Q

Substitute P = 5700 and Q = 2640 in the above equation.

R = P – Q

R = 5700 – 2640

R = 3060

The final answer is R = 3060

7. In F = 5/2 (T – 32) find F if T = 64?

## Solution:

Given that F = 5/2 (T – 32)

To find F, rewrite the given equation by changing the subject to F.

F = 5/2 (T – 32)

Substitute T = 64 in the above equation.

F = 5/2 (T – 32)

F = 5/2 (64 – 32)

F = 5/2 (32)

F = 5 × 16 = 80

F = 80

The final answer is F = 80.

8. In Q = a × b × c find a if Q = 4000, b = 10, c = 10?

## Solution:

Given that Q = a × b × c

To find a, rewrite the given equation by changing the subject to a.

Q = a × b × c

Move bc to the left side and divide it from Q

Q/bc = a

a = Q/bc

Substitute Q = 4000, b = 10, c = 10 in the above equation.

a = 4000/(10 × 10)

a = 4000/100 = 40

The final answer is a = 40

9. If G = 2k find k if G = 70?

## Solution:

Given that G = 2k

To find k, rewrite the given equation by changing the subject to k.

G = 2k

Move 2 to the left side and divide it from G

G/2 = k

k = G/2

Substitute G = 70 in the above equation.

k = 70/2

k = 35

The final answer is k = 35.

10. If n + o + p = 190 find o if n = 60 and p = 55?

## Solution:

Given that n + o + p = 190

To find o, rewrite the given equation by changing the subject to o.

n + o + p = 190

Move n + p to the right side and subtract it from 190.

o = 190 – (n + p)

Substitute n = 60 and p = 55 in the above equation.

0 = 190 – (60 + 55)

o = 190 – 115

o = 75

The final answer is o = 75

11. In a = x + yz find z if a = 54, x = 12 and y = 3?

## Solution:

Given that a = x + yz

To find z, rewrite the given equation by changing the subject to z.

a = x + yz

Move x to the left side and subtract it from a

a – x = yz

Move y to the left side and divide it from a – x

(a – x)/y = z

z = (a – x)/y

Substitute a = 54, x = 12 and y = 3 in the above equation.

z = (54 – 12)/3

z = 42/3

z = 14

The final answer is z = 14.

12. In rs²/4π² = m, find the value of s if m = 49, r = 4?

## Solution:

Given that rs²/4π² = m

To find s, rewrite the given equation by changing the subject to s.

rs²/4π² = m

Move 4π² to the right side and multiply it with m

rs² = m(4π²)

Move r to the right side and divide it from m(4π²)

s² = m(4π²)/r

Substitute m = 49, r = 4 in the above equation. π² = 9.8

s² = 49(4 × 9.8)/4

s² = 480.2

s = √480.2

s = 21.91

The final answer is s = 21.91(approximately)

13. In Y = 2x (m + n), find x if Y = 50, m = 6, n = 4?

## Solution:

Given that Y = 2x (m + n),

To find x, rewrite the given equation by changing the subject to x.

Y = 2x (m + n)

Move 2(m + n) to the left side and divide it by Y

Y/(2(m + n)) = x

x = Y/(2(m + n))

Substitute Y = 50, m = 6, n = 4 in the above equation.

x = 50/(2(6 + 4))

x = 50/2(10)

x = 50/20

x = 5/2

The final answer is x = 5/2

14. In L = m/2 {2b + (m – 1) d}, find d when L = 125, m = 10, b = 2?

## Solution:

Given that L = m/2 {2b + (m – 1) d}

To find d, rewrite the given equation by changing the subject to d.

L = m/2 {2b + (m – 1) d}

Move 2 to the left side and multiply it with the 2.

2L = m{2b + (m – 1) d}

Move m to the left side and divide it with the 2L.

2L/m = 2b + (m – 1) d

Move 2b to the left side and subtract it from the 2L/m.

2L/m – 2b = (m – 1) d

Move m – 1 to the left side and divide it from the 2L/m – 2b.

(2L/m – 2b)/(m – 1) = d

d = (2L/m – 2b)/(m – 1)

Substitute L = 125, m = 10, b = 2 in the above equation.

d = (2(125)/10 – 2(4))/(10 – 1)

d = (250/10 – 8)/9

d = (25 – 8)/9

d = 17/9

The final answer is d = 17/9.

15. If T = 2 πr, find r if T = 88, π = 22/7?

## Solution:

Given that T = 2 πr

To find r, rewrite the given equation by changing the subject to r.

T = 2 πr

Move 2 π to the left side and divide it from the T

T/2 π = r

r = T/2 π

Substitute T = 88, π = 22/7 in the above equation.

r = 88/2(22/7)

r = 88/(44/7) = 88 × 7/44 = 2 × 7 = 14

r = 14

The final answer is r = 14.

16. If S = H × R, find H when S = 450 and R = 15?

## Solution:

Given that S = H × R

To find H, rewrite the given equation by changing the subject to H.

S = H × R

Move R to the left side and divide it from the S

S/R = H

H = S/R

Substitute S = 450 and R = 15 in the above equation.

H = 450/15

H = 30

The final answer is H = 30.

17. In c = (l – m)/(l + m), if c = 3/7 and l = 10, find m?

## Solution:

Given that c = (l – m)/(l + m)

To find m, rewrite the given equation by changing the subject to m.

c = (l – m)/(l + m)

Move l + m to the left side and multiply it with the c.

c(l + m) = l – m

cl + cm = l – m

Move cl to the right side and m to the left side with proper opertaions.

cm + m = l – cl

m(c + 1) = l (1 – c)

Move (1 + c) to the right side and divide it by l (1 – c)

m = l (1 – c)/(1 + c)

Substitute c = 3/7 and l = 10 in the above equation.

m = 10 (1 – 3/7)/(1 + 3/7)

m = 10 (0.4)

m = 4

The final answer is m = 4

18. If R = (A × G × E)/100, find G if R = 80, A = 400, E = 10?

## Solution:

Given that R = (A × G × E)/100

To find G, rewrite the given equation by changing the subject to G.

R = (A × G × E)/100

Move 100 to the left side and multiply it with the R.

100R = A × G × E

Move AE to the left side and divide it with the 100R.

100R/AE = G

G = 100R/AE

Substitute R = 80, A = 400, E = 10 in the above equation.

G = 100(80)/(400)(10)

G = 8000/4000

G = 2

The final answer is G = 2.

19. In A/B = 100, find B if A = 200?

## Solution:

Given that A/B = 100

To find B, rewrite the given equation by changing the subject to B.

A/B = 100

Move B to the right side and multiply it by 100.

A = 100B

Move 100 to the left side and divide it with the A.

A/100 = B

B = A/100.

Substitute A = 200 in the above equation.

B = 200/100

B = 2

The final answer is B = 2.

20. In PQR/T = AB, find B. if P = 2, Q = 3, R = 4, T = 4, A = 2?

## Solution:

Given that PQR/T = AB.

To find B, rewrite the given equation by changing the subject to B.

PQR/T = AB

Move A to the left side and divide it from the PQR/T.

B = APQR/T

Substitute P = 2, Q = 3, R = 4, T = 4, A = 2 in the above equation.

B = (4 × 2 × 3 × 4)/4 = 24

B = 24.

The final answer is B = 24.