Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.Let x = the number of packages of pasta and y = the number of jars of pasta sauce.One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry?How many packages of pasta?How many jars of pasta sauce?Explain your reasoning.
Question
Tyler went to the supermarket to buy food for a food pantry. He has 1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.Let x = the number of packages of pasta and y = the number of jars of pasta sauce.One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry?How many packages of pasta?How many jars of pasta sauce?Explain your reasoning.
Solution
To solve this problem, we need to consider both the budget and the weight limit.
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First, let's consider the budget. Tyler has 1. If he buys only pasta sauce, he can buy 12 jars because each jar costs $3.
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However, we also need to consider the weight limit. Tyler can carry up to 20 pounds. If he buys only pasta, he can buy 20 packages because each package weighs 1 pound. If he buys only pasta sauce, he can buy 13 jars because each jar weighs 1.5 pounds and 13 jars would weigh 19.5 pounds, which is under the 20 pound limit.
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Since one package of pasta is the right amount to go with one jar of pasta sauce, we need to find a balance between the two.
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If Tyler buys 12 packages of pasta and 12 jars of pasta sauce, he would spend 1 + 12*$3) and carry 18 pounds of food (121 pound + 121.5 pounds), which is under his budget and weight limit.
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Therefore, the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry are 12 each. This way, Tyler can maximize the amount of food he buys while staying within his budget and weight limit.
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