Studdy AI Logo
Math

Question A patient weighing 195 lbs requires 279 mg of medicine. Find the amount of medicine required for a patient weighing 130 lbs.

Studdy Solution

STEP 1

Assumptions
1. The amount of medicine is directly proportional to the patient's body weight.
2. A patient weighing 195 pounds requires 279 milligrams of medicine.
3. We need to find the amount of medicine required for a patient weighing 130 pounds.

STEP 2

Since the amount of medicine is directly proportional to the patient's body weight, we can set up a proportion to solve for the unknown amount of medicine.
Amount of medicine for first patientWeight of first patient=Amount of medicine for second patientWeight of second patient\frac{Amount\, of\, medicine\, for\, first\, patient}{Weight\, of\, first\, patient} = \frac{Amount\, of\, medicine\, for\, second\, patient}{Weight\, of\, second\, patient}

STEP 3

Now, plug in the known values for the first patient and the known weight for the second patient into the proportion.
279 mg195 lbs=x mg130 lbs\frac{279\, mg}{195\, lbs} = \frac{x\, mg}{130\, lbs}
Here, xx represents the unknown amount of medicine for the second patient weighing 130 pounds.

STEP 4

To find xx, we need to cross-multiply the values in the proportion.
279 mg×130 lbs=195 lbs×x mg279\, mg \times 130\, lbs = 195\, lbs \times x\, mg

STEP 5

Perform the multiplication on both sides of the equation.
36270 mg⋅lbs=195 lbs⋅x mg36270\, mg \cdot lbs = 195\, lbs \cdot x\, mg

STEP 6

Now, we need to isolate xx to solve for the amount of medicine required by the second patient. We do this by dividing both sides of the equation by the weight of the first patient (195 pounds).
36270 mg⋅lbs195 lbs=195 lbs⋅x mg195 lbs\frac{36270\, mg \cdot lbs}{195\, lbs} = \frac{195\, lbs \cdot x\, mg}{195\, lbs}

STEP 7

Simplify both sides of the equation to solve for xx.
x=36270 mg⋅lbs195 lbsx = \frac{36270\, mg \cdot lbs}{195\, lbs}

STEP 8

Perform the division to find the value of xx.
x=36270 mg195x = \frac{36270\, mg}{195}

STEP 9

Calculate the value of xx.
x=186 mgx = 186\, mg
The patient weighing 130 pounds requires 186 milligrams of medicine.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord