Math  /  Numbers & Operations

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To control an infection, a doctor recommends that a patient who weighs 92 pounds be given 320 milligrams of antibiotic. If the antibiotic is given proportionally according to the patient's weight, how much antibiotic should to a patient who weighs 138 pounds? 400 milligrams 480 milligrams 550 milligrams 600 milligrams

Studdy Solution

STEP 1

What is this asking? If a 92-pound patient needs 320mg of medicine, how much medicine does a 138-pound patient need? Watch out! Make sure to set up the proportion correctly – weight to medicine, weight to medicine!

STEP 2

1. Set up a proportion
2. Solve for xx

STEP 3

Let xx be the amount of antibiotic needed for the 138-pound patient.
We're trying to find xx!

STEP 4

We can set up a proportion relating the weight of each patient to the amount of antibiotic they need.
The proportion will look like this: weight of patient 1antibiotic for patient 1=weight of patient 2antibiotic for patient 2\frac{\text{weight of patient 1}}{\text{antibiotic for patient 1}} = \frac{\text{weight of patient 2}}{\text{antibiotic for patient 2}}.

STEP 5

We know that a 92-pound patient needs 320mg of antibiotic, and we want to find the amount needed for a 138-pound patient.
So, our proportion becomes 92320=138x\frac{92}{320} = \frac{138}{x}.
See how we kept the units consistent – pounds on top, milligrams on the bottom!

STEP 6

**Cross-multiply** to get rid of the fractions!
Multiply 9292 by xx and 320320 by 138138.
This gives us 92x=32013892 \cdot x = 320 \cdot 138.

STEP 7

Now, we simplify the right side: 92x=4416092x = 44160.

STEP 8

To **isolate** xx, we need to **divide** both sides of the equation by **92**.
Remember, we're dividing by 92 to multiply by 192\frac{1}{92} to turn the 92 on the left into a 1!
So we get x=4416092x = \frac{44160}{92}.

STEP 9

Finally, we calculate the value of xx: x=480x = 480.
So, a 138-pound patient needs **480mg** of antibiotic.

STEP 10

The 138-pound patient needs 480 milligrams of antibiotic.

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