A patient complaining of restlessness drinks 5 12-oz cups of coffee each day. If the doctor recommends cutting the coffee intake back by 60%, how many ounces of coffee can the patient have each day?

We can solve this problem by calculating how many ounces of coffee the patient drinks each day, and then calculating how many ounces they are allowed to drink. Since we are told they need to cut back 60%, this means they are allowed to drink 100% – 60% = 40% of their current daily intake.
Step 1: Calculate the total number of ounces of coffee the patient currently drinks.
\(5cups \times 12ounces=60 ounces\)
Step 2: Use the percent formula to calculate how much of the current 60 ounces the patient is allowed to drink. The percent formula is below: \(\frac{\mathrm{part} }{\mathrm{whole}} = \frac{\mathrm{ \% } }{\mathrm{100}}\)
We know that the current “whole” is 60 oz. We also know that, since they need to cut back by 60%, they are only permitted to drink 100% – 60% = 40% of the current whole value. We are searching for “part”, so that is where we will place our x.
\(\frac{\mathrm{x} }{\mathrm{60}} = \frac{\mathrm{40} }{\mathrm{100}}\)
Step 3: Cross multiply.
\(100x= 60 \times 40\)
Step 4: Simplify the right side of the equation
100x=2.400
Step 5: Simplify by dividing both sides of the equation by 100.
\(\frac{\mathrm{100x} }{\mathrm{100}}= \frac{\mathrm{2.400} }{\mathrm{100}}\)
\(x=24\)
Read the problem carefully. Many people fall into the trap of solving for 60%. However, this is how much the patient needs to cut back, not how much they are allowed to drink, which is what the problem asks.