Question 514565: how to solve the problem: Nature Drinks wants to combine orange juice they will sell for $0.09 per ounce with guava juice they sell for $0.14 per ounce to create an orange guava drink. how many ounces of orange should they use to create a 16 ounce drink that will sell for $1.74
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let o equal the unknown number of ounces of orange juice in a 16 ounce drink and let g equal the unknown number of ounces of guava juice in a 16 ounce drink. Since there are two unknowns, we need to have two independent equations to solve this problem.
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The first equation comes from the fact that the two unknown number of ounces (o and g) must add up to a total of 16 ounces. Therefore, we can write the first equation as:
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Next, we can write a selling cost equation. We know that selling cost per ounce of orange juice is $0.09 (which is 9 cents). So for o ounces of orange juice, we would multiply o times $0.09 per ounce to get the selling cost. Similarly, the selling cost per ounce of guava juice is $0.14 (14 cents) per ounce. So the selling cost for g ounces of guava juice is found by multiplying $0.14 times g. To find the total selling cost of the 16 ounce drink (which we know to be $1.74) we can write the second of our two equations as:
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to get rid of the decimals and make things a little easier, let's multiply this second equation (all terms and both sides) by 100 to get:
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So our two equations are:
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Let's solve this by substitution. Using the first equation, we can subtract g from both sides to get:
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Then in the second equation we can substitute 16 - g for o since they are equal. With this substitution the second equation becomes:
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Do the distributed multiplication by multiplying 9 times each of the two terms in the parentheses to get:
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Subtract 144 from both sides and you have:
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Combine the two terms on the left side:
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And solve for g by dividing both sides of this equation by 5 to get:
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We now know that in a 16 ounce drink there must be 6 ounces of guava juice. And since the rest of the 16 ounce drink is orange juice, we know there must be 10 ounces of orange juice.
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You can check this answer by multiplying 14 cents times the 6 ounces of guava juice, multiplying 9 cents times the 10 ounces of orange juice, and make sure this totals to the selling price of 174 cents ($1.74).
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Hope this helps you to understand the problem a little better.
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