A certain medicine is given in the amount proportional to a patient's body weight. Suppose a patient weighing 164 pounds requires a 205 milligram of medicine. What is the weight of a patient who requires 173.75 milligrams of medicine?
Set up a proportion equation:
m = kw, where m is the amount of medicine, and w is the body weight, k is a constant
for m = 205, w = 164
205 = k(164)
k = 205/164 = 5/4
m = (5/4)w
when m = 173.75,
173.75 = (5/4)w
w = 139
or
just use a simple ratio:
w/164 = 173.75/205
w = 164(173.75/205)
= 139
Well, let's do some prescription math, shall we? If the amount of medicine is proportional to the patient's body weight, we can set up a ratio. If 164 pounds requires 205 milligrams, then we can write it as 164 pounds is to 205 milligrams. Now, we can find out the weight of a patient who requires 173.75 milligrams. Let's call it x pounds.
So, we have the ratio: 164 pounds / 205 milligrams = x pounds / 173.75 milligrams
Now, cross-multiply and solve for x: 164 pounds * 173.75 milligrams = x pounds * 205 milligrams
41,740 pounds * milligrams = x pounds * milligrams
Now, divide both sides by milligrams: 41,740 pounds = x pounds
So, a patient who requires 173.75 milligrams of medicine would weigh approximately 41,740 pounds. Just kidding! That would be one hefty patient! The weight is 173.75 pounds. There you have it, one prescription punchline served right up!
To find the weight of the patient who requires 173.75 milligrams of medicine, we can set up a proportion using the given information.
Let's denote the weight of the patient as "x" and the amount of medicine required as "y".
According to the problem, the ratio of weight to medicine is constant for the two cases:
weight1 / medicine1 = weight2 / medicine2
Plugging in the given values:
164 pounds / 205 milligrams = x pounds / 173.75 milligrams
We can cross-multiply to solve for x:
164 pounds * 173.75 milligrams = 205 milligrams * x pounds
Using unit conversion to ensure the units cancel out:
(164 pounds * 173.75 milligrams) / (205 milligrams) = x pounds
Calculating:
x = (28490 pounds*milligrams) / (205 milligrams)
x = 139.2195122 pounds
Therefore, the weight of the patient who requires 173.75 milligrams of medicine is approximately 139.22 pounds.
To solve this problem, we can set up a proportion using the given information:
Weight1 / Medicine1 = Weight2 / Medicine2
Let's assign variables to the given weights and medicines:
Weight1 = 164 pounds
Medicine1 = 205 milligrams
Weight2 is unknown, and Medicine2 is given as 173.75 milligrams.
Now we can plug in the values into the proportion:
164 / 205 = Weight2 / 173.75
To find Weight2, we can cross-multiply and solve for it:
164 * 173.75 = Weight2 * 205
28465 = Weight2 * 205
Now divide both sides of the equation by 205 to isolate Weight2:
Weight2 = 28465 / 205
Weight2 ≈ 138.90 pounds
Therefore, a patient who requires 173.75 milligrams of medicine would weigh approximately 138.90 pounds.