SOLUTION: an ice cream parlor buys 15 pounds of hot fudge to prepare 525 hot fudge sundaes. at this rate how many sundaes can be made with 20 pound of hot fudge?

Question 508120: an ice cream parlor buys 15 pounds of hot fudge to prepare 525 hot fudge sundaes. at this rate how many sundaes can be made with 20 pound of hot fudge?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
One way to do this problem is using a proportion. In a proportion we set two ratios (or fractions) equal. For this proportion, let's use the pounds of hot fudge as the numerators and the corresponding number of sundaes as the denominators.
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For the first ratio or fraction, we know that 15 pounds of hot fudge relates to 525 sundaes. So we can write this fraction as:
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For the second ratio or fraction, we are given 20 pounds of hot fudge and we want to know the number of sundaes it compares to. Call the unknown number of sundaes for this ratio N. Therefore, in this ratio, 20 is the numerator and N is the denominator. So this ratio is:
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To solve we begin by setting the ratios equal to get the proportion:
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You can begin to solve proportions by cross-multiplying. This means that we multiply the numerator on one side by the denominator on the other side, and we do this for both numerators. Then we set the two products equal and solve. This results in the cross-multiplication and equality as follows:
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To solve this equation, divide both sides by 15 to get:
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Multiply out the numerator:
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And dividing out the right side (15 into 10500) results in:
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The answer is that if 15 lbs makes 525 sundaes, then 20 lbs will make 700 sundaes.
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Hope this helps you to understand the problem a little better. When you do proportions, just keep them straight by making the units the same on the two numerators, make the units the same on the two denominators, and ensure that the numerator on the left side relates to the denominator on the left side. And ensure on the right side that the numerator corresponds to the denominator. (In this problem, the 15 lbs on the left side corresponded to the 525 sundaes. And on the right side the 20 lbs corresponded to the unknown number of sundaes.) Other than that, just follow the rule of cross-multiplying (left numerator times right denominator and then right numerator times left denominator). Set these two cross-products equal and solve. (And the unknown can be in any of the four positions ... left numerator or right numerator or left denominator or right denominator ... wherever it appears in the ratio. The cross-multiplication takes that into consideration. Just multiply crossways and set the products equal. A little practice will build your confidence in the method. Good luck.
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