Jennifer went to the post office for stamps. She bought the same number of 8-cent stamps and 10-cent stamps. She also bought as many 2-cent stamps as both of the other two kinds combined. How many of each kind did she get if she paid a total of $4.40 for them all?<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Let’s break down the problem step by step to find out how many stamps Jennifer bought of each kind.<\/p>\n\n\n\n Let xx be the number of 8-cent stamps<\/strong> she bought. She bought as many 2-cent stamps<\/strong> as the total of the 8-cent and 10-cent stamps<\/strong>, which means she bought 2x2x 2-cent stamps<\/strong>.<\/p>\n\n\n\n Now we calculate the cost of each type of stamp:<\/p>\n\n\n\n Add them up for total cost in cents<\/strong>: 8x+10x+4x=22x cents8x + 10x + 4x = 22x \\text{ cents}<\/p>\n\n\n\n We are told the total cost is $4.40, which is 440 cents<\/strong>.<\/p>\n\n\n\n So we set up the equation: 22x=44022x = 440<\/p>\n\n\n\n x=44022=20x = \\frac{440}{22} = 20<\/p>\n\n\n\n This problem involves simple algebra and a good understanding of how to translate words into mathematical expressions. Jennifer bought three types of stamps with different costs and in quantities related to each other. By carefully assigning a variable to the number of one type of stamp (8-cent), we were able to express the other two types in terms of that same variable. The 10-cent stamps were bought in the same quantity as the 8-cent stamps, so both were represented by the variable xx. The 2-cent stamps were bought in an amount equal to the total of the other two kinds, meaning she got x+x=2xx + x = 2x of those.<\/p>\n\n\n\n Next, we calculated the cost of each type of stamp. Since costs were in cents, we kept all calculations in cents to match the $4.40 total, which equals 440 cents. Adding all the costs together gave us a simple equation, 22x=44022x = 440, which we solved by dividing both sides by 22. The result, x=20x = 20, tells us she bought 20 of each of the 8- and 10-cent stamps, and 2x=402x = 40 of the 2-cent stamps.<\/p>\n\n\n\n This type of problem is a classic example of using variables and equations to model a real-life situation. It teaches the importance of organizing information and being careful with units (like cents vs. dollars).<\/p>\n","protected":false},"excerpt":{"rendered":" Jennifer went to the post office for stamps. She bought the same number of 8-cent stamps and 10-cent stamps. She also bought as many 2-cent stamps as both of the other two kinds combined. How many of each kind did she get if she paid a total of $4.40 for them all? The correct answer […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-16935","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16935","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=16935"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16935\/revisions"}],"predecessor-version":[{"id":16936,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16935\/revisions\/16936"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=16935"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=16935"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=16935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Define the variables<\/h3>\n\n\n\n
Then she also bought x<\/strong> 10-cent stamps<\/strong>, since it says the same number.<\/p>\n\n\n\n
\n\n\n\nStep 2: Total cost equation<\/h3>\n\n\n\n
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\n\n\n\nStep 3: Solve for xx<\/h3>\n\n\n\n
\n\n\n\nStep 4: Final Answer<\/h3>\n\n\n\n
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\n\n\n\nExplanation (300 words)<\/h3>\n\n\n\n