Lemonade ProportionsDate: 04/02/98 at 20:50:01 From: Ria Evans Subject: Algebra Making lemonade requires water and lemon juice in the ratio of 3 cups of water to 2 cups of lemon juice. You need a total of 10 gallons for the fair. How many cups of lemon juice do you need? If you made 10 gallons of lemonade for your class, how much would each person get? (Hint: 16 C = 1 gal). Date: 04/04/98 at 15:23:09 From: Doctor Scott Subject: Re: Algebra Hi Ria! We know we want to make 160 cups of lemonade for the fair. We can use some algebra to solve the problem. Every 5 cups of lemonade require 3 cups of water and 2 cups of lemon juice. We can use a proportion to help us: 3 cups water ? cups of water ------------------ = -------------------- 5 cups of lemonade 160 cups of lemonade Notice that the proportion allows us to compare the amounts of water and lemonade. We can compare the known ratio (3 to 5) to the one we want to make (? to 160), with the amount of water in the numerator and the total amount of lemonade in the denominator. Remember that we solve proportions by cross multiplying. (I'm going to replace the ? with "x"): 3 * 160 = 5x 480 = 5x 96 = x <-- so we need 96 cups of water Then, we know we are going to get 160 cups of lemonade, so we need: 160 - 96 = 64 cups of lemon juice. We could have found the amount of lemon juice first, again by using a proportion to compare the quantities: 2 cups lemon juice ? cups lemon juice ------------------ = ------------------- 5 cups of lemonade 160 cups lemonade cross multiplying: 320 = 5x 64 = x <--- amount of lemon juice We can also check our answer. We need a ratio of 3:2, and we have 96 cups water ------------------- 64 cups lemon juice Is this fraction equal to 3/2? If so, then we're okay! Proportions are a great way to solve a lot of problems. Whenever a problem involved comparing quantities, I usually try to use a proportion! Hope this helps! -Doctor Scott, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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