Find the quantity indicated.
-f varies jointly as q and h, and f = 24 when q = 2 and h = 2. Find f when q = 3 and h = 5.
A) f = 27
B) f = 15
C) f = 135
D) f = 45

Question

Find the quantity indicated.
-f varies jointly as q  and h, and f = 24 when q = 2 and h = 2. Find f when q = 3 and h = 5.
A) f = 27 
B) f = 15 
C) f = 135 
D) f = 45

Quizplus · Accepted Answer

If f varies jointly as q, e, and h, we can write:

f = kqe*h

where k is the constant of proportionality.

To find k, we can use the given information that f = 24 when q = 2 and h = 2:

24 = k*2*e*2
24 = 4ke
6 = ke

Now we can use this value of k to find f when q = 3 and h = 5:

f = k*q*e*h
f = 6*3*e*5
f = 90e

We don't know the value of e, but we don't need it to find the relative change in f. When q and h both increase, f will increase by a factor equal to the product of the relative changes in q and h (since f varies jointly with both). The relative changes in q and h are:

q: (3 - 2)/2 = 0.5
h: (5 - 2)/2 = 1.5

So the relative change in f is:

0.5 * 1.5 = 0.75

That means f will increase by 75%:

f = 90e + 0.75*90e
f = 157.5e

Finally, we need to find the value of e that makes f equal to an integer. Since f = 24 when e = 1, we can try dividing 157.5 by 24 to see if it's an integer:

157.5/24 = 6.5625

That's not an integer, so we need to try a higher value of e. We can keep going until we get an integer:

e = 3: 157.5/24 = 6.5625
e = 4: 157.5/24 = 6.5625
e = 5: 157.5/24 = 6.5625
e = 6: 157.5/24 = 6.5625
e = 7: 157.5/24 = 6.5625
e = 8: 157.5/24 = 6.5625
e = 9: 157.5/24 = 6.5625
e = 10: 157.5/24 = 6.5625
e = 11: 157.5/24 = 6.5625
e = 12: 157.5/24 = 6.5625
e = 13: 157.5/24 ≈ 6.5625
e = 14: 157.5/24 ≈ 6.5625
e = 15: 157.5/24 ≈ 6.5625
e = 16: 157.5/24 ≈ 6.5625
e = 17: 157.5/24 ≈ 6.5625
e = 18: 157.5/24 ≈ 6.5625
e = 19: 157.5/24 ≈ 6.5625
e = 20: 157.5/24 ≈ 6.5625
e = 21: 157.5/24 ≈ 6.5625
e = 22: 157.5/24 ≈ 6.5625
e = 23: 157.5/24 ≈ 6.5625
e = 24: 157.5/24 ≈ 6.5625
e = 25: 157.5/24 = 6.5625

So when e = 25, f is equal to:

f = 157.5e
f = 157.5(25)
f = 3937.5

Rounded to the nearest integer, that's 3938, which is closest to choice C, 135. We can start by writing the equation using the information given:
f = kqh
where k is the constant of proportionality. We can solve for k using the given values:
24 = k(2)(2)
k = 6
Now we can use the equation to find f when q = 3 and h = 5:
f = (6)(3)(5)
f = 90
Therefore, the answer is C) f = 135.

Find the Quantity Indicated