Solved on Jan 26, 2024

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

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.
$\frac{Amount\, of\, medicine\, for\, first\, patient}{Weight\, of\, first\, patient} = \frac{Amount\, of\, medicine\, for\, second\, patient}{Weight\, of\, second\, patient}$

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

Now, we need to isolate $x$ 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).
$\frac{36270\, mg \cdot lbs}{195\, lbs} = \frac{195\, lbs \cdot x\, mg}{195\, lbs}$

STEP 7

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

STEP 8

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

STEP 9

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

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

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

Now, we need to isolate $x$ 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).
$\frac{36270\, mg \cdot lbs}{195\, lbs} = \frac{195\, lbs \cdot x\, mg}{195\, lbs}$

STEP 7

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

STEP 8

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

STEP 9

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

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

STEP 1

Assumptions1. 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

STEP 3

STEP 4

To find xxx, 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\, mg279mg×130lbs=195lbs×xmg

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\, mg36270mg⋅lbs=195lbs⋅xmg

STEP 6

STEP 7

Simplify both sides of the equation to solve for xxx.x=36270 mg⋅lbs195 lbsx = \frac{36270\, mg \cdot lbs}{195\, lbs}x=195lbs36270mg⋅lbs​

STEP 8

Perform the division to find the value of xxx.x=36270 mg195x = \frac{36270\, mg}{195}x=19536270mg​

STEP 9

Calculate the value of xxx.x=186 mgx = 186\, mgx=186mgThe patient weighing 130 pounds requires 186 milligrams of medicine.

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

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.

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

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

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

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

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