A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing
119
pounds requires
136
milligrams of medicine. What is the weight of a patient who requires
200
milligrams of medicine?
To find the weight of a patient who requires 200 milligrams of medicine, we can use the proportional relationship between weight and medicine dosage.
Let's set up a proportion:
Weight_1 / Dosage_1 = Weight_2 / Dosage_2
Using the given information:
Weight_1 = 119 pounds
Dosage_1 = 136 milligrams
Dosage_2 = 200 milligrams
Plugging in the values into the proportion:
119 / 136 = Weight_2 / 200
To solve for Weight_2, we need to isolate it on one side of the equation. Cross-multiplying:
Weight_2 = (119 * 200) / 136
Calculating this expression:
Weight_2 ≈ 174.853 pounds
Therefore, the weight of a patient who requires 200 milligrams of medicine is approximately 174.853 pounds.
To solve this problem, we can set up a proportion using the given information.
Let's denote the weight of the patient who requires 200 milligrams of medicine as x.
According to the problem, the amount of medicine is proportional to the body weight.
So, we can set up the proportion as follows:
119 pounds / 136 milligrams = x pounds / 200 milligrams
To solve for x, we can cross-multiply and then solve for x.
(119 pounds)(200 milligrams) = (136 milligrams)(x pounds)
23,800 pounds*milligrams = 136x pounds*milligrams
Now, we can cancel out the units of pounds*milligrams on both sides of the equation.
23,800 = 136x
To isolate x, divide both sides of the equation by 136.
23,800 / 136 = x
x ≈ 175
Therefore, a patient who requires 200 milligrams of medicine would weigh approximately 175 pounds.
119/136 = x/200
Cross multiply and solve for x.