1. ## Partial variation

Hi, I have an exam in two days involving a few areas of math and unfortunately I have NOT studied for it at all (not something I usually do but I had other subjects that needed to be prioritised). Here is one of the problems I am having trouble with. If it's okay, I'd like to see a complete worked out example for future reference.

If A varies partly with B, and A=15 when B=2, and A= 27 when B= 5, find A when B=10

And I emphasize, any help will be strongly appreciated!

2. ....partly with B.
So B is part of a quantity.
Let that quantity be (B +u).
Hence, A = k(B +U) -----------------(i)
where k = constant of variation

When A = 15, and B = 2
15 = k(2 +u) --------------(1)

When A = 27, and B = 5
27 = k(5 +u) --------------(2)

Solve (1) and (2) simultaneously and you'd get
u = 7/4
and k = 4

So, when B = 10,
A = 4(10 +7/4)

3. What do you mean solve (1) and (2) simultaneously? I don't understand...How did you get 7/4?

4. Originally Posted by Joker37
What do you mean solve (1) and (2) simultaneously? I don't understand...How did you get 7/4?
You have not encountered yet solving equations simultaneously?
Incredible.

Anyway, "solving simultaneously" here means solving for the values of the unknowns that will satisfy the many equations simultaneously. Or, the k of one equation is also the same k of the other equation. The u of one equation is the equal to the u of the other equation. Etc...

Or, you find the intersection points of the many equations.

:-), I think you're more lost now than before you read the above.

15 = k(2 +u) --------------(1)
27 = k(5 +u) --------------(2)

15 = 2k +uk ------------(1a)
27 = 5k +uk ------------(2a)

To eliminate uk, subtract (1a) from (2a),
12 = 3k
k = 12/3 = 4 ---------**

Substitute that into, say, (1),
15 = 4(2 +u)
15 = 8 +4u
15 -8 = 4u
u = 7/4 -----------**

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# partial variation word problems worksheet

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