Acid Concentration, Heating Bill
Date: 7/6/96 at 12:58:17 From: Alfred T Chu Subject: Acid Concentration, Heating Bill Hello Math wizard! Well, I have two algebra word problems: 1. A pharmacist has 8 liters of a 15 percent solution of acid. How much distilled water must she add to reduce the concentration of acid to 10 percent? 2. By installing a $120 thermostat that reduces the temperature setting at night, a family hopes to cut its annual bill for heating oil by 8 percent, and thereby recover the cost of the thermostat in fuel savings after 2 years. What was the family's annual fuel bill before installing the thermostat? Can you show me how to do these and the logic behind them? I want be able to do 'em later on myself. Thank you very much. Take care, Alfred
Date: 7/6/96 at 15:8:45 From: Doctor Paul Subject: Re: Acid Concentration, Heating Bill Number 1: You begin with 8 liters of a 15 percent solution. That means you have 15 percent acid and 85 percent water, right? Let's figure out how many liters of acid and water you have to begin with. 15 percent of 8 is 1.2 (.15*8) liters. So you've got 1.2 liters of acid and 6.8 liters of water (8-1.2 = 6.8). Now you want to add water until the concentration is down to 10 percent. Note that the amount of acid will remain constant..you're only changing the amount of water. You want 1.2 liters of acid to be 10 percent of the entire quantity. Set up a proportion to find out how much is 100 percent of the quantity. 10 percent 100 percent ---------- = ----------- 1.2 liters x liters now cross multiply: 1.2 = .1*x divide both sides by .1 and you get: 12 = x So 12 liters is the entire amount of solution that makes 1.2 liters 10% of the concentration. Now read the problem. It asks how much diltilled water must be added to make the concentration 10 percent. You go from 8 liters to 12 liters so that's 4 liters of water. Number 2: The family wants to save $120 over a period of two years. That means they want to save $60 a year, right? The problem also states they want to cut their yearly bill by 8 percent. Well, the two paragraphs above tell you what you need to know...that $60 is 8 percent of the total bill. Let's set up a proportation and solve for the total bill: 60 x --------- = ----------- 8 percent 100 percent cross multiply: 60 = .08*x divide both sides by .08 750 = x The total yearly bill is $750. Let's check the answer. The family wants to save $120 over two years by saving 8 percent each year. Well, 8 percent of $750 is $60 so the new bill will be $690 per year. Over two years, that adds up to $120 in savings. -Doctor Paul, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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