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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.