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A a varies partly with B and with another quantity C. If the to when B=2 and A= 28 and A = 12 when B = 3 and C=26. Find the value of A when B = 4 and C=6 Find the value of B when A= 38 and C=6​

User Ahmed Hany
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To solve this problem, we can use a system of two equations with two unknowns, based on the information given.

Let x be the part of A that varies with B, and y be the part of A that varies with C. Then we have:

A = xB + yC

Using the values given in the problem, we can write two equations:

When B = 2 and A = 28:
28 = 2x + 0y (since C is not mentioned)

When B = 3 and C = 26 and A = 12:
12 = 3x + 26y

Now we can solve for x and y by solving the system of equations:

2x = 28 => x = 14
3x + 26y = 12 => 42 + 26y = 12 => 26y = -30 => y = -15/13

Therefore, we have:

A = 14B - 15/13C

a) To find the value of A when B=4 and C=6, we can substitute B=4 and C=6 into the equation:

A = 14(4) - 15/13(6) = 56 - 45/13 = 383/13

Therefore, A is equal to 383/13 when B=4 and C=6.

b) To find the value of B when A=38 and C=6, we can rearrange the equation to solve for B:

A = 14B - 15/13C => 13A = 182B - 15C => 13A + 15C = 182B

Substituting A=38 and C=6, we have:

13(38) + 15(6) = 182B => 494 = 182B => B = 247/91

Therefore, B is equal to 247/91 when A=38 and C=6.
User Drnugent
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