a,b and c are real numbers such that ab=44, bc=112 and a+c=13. What is the value of b?
a = 44/b
c = 112/b
so
44/b + 112/b = 13
156 = 13 b
b = 12
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To find the value of b, we need to use the given equations and solve for b.
We are given that ab = 44 and bc = 112. Since these equations involve b, we can try to eliminate b by dividing them.
Dividing the equation ab = 44 by the equation bc = 112, we get:
(ab) / (bc) = 44 / 112
Simplifying both sides of the equation gives:
a / c = 11 / 28
Now, we are given that a + c = 13. We can use this information to eliminate one variable from the equation a / c = 11 / 28.
Rearranging the equation a + c = 13, we get:
a = 13 - c
Substituting this into the equation a / c = 11 / 28, we get:
(13 - c) / c = 11 / 28
Cross multiplying gives:
28(13 - c) = 11c
Expanding both sides of the equation gives:
364 - 28c = 11c
Adding 28c to both sides of the equation gives:
364 = 39c
Dividing both sides of the equation by 39 gives:
c = 364 / 39
Simplifying gives:
c = 32 / 3
Now that we have the value of c, we can substitute it back into one of the original equations to solve for b. Let's use the equation bc = 112:
b(32 / 3) = 112
Multiplying both sides of the equation by 3/32 gives:
b = (112 * 3) / 32
Simplifying gives:
b = 336 / 32
Reducing the fraction gives:
b = 21 / 2
Therefore, the value of b is 21/2 or 10.5.