{"id":32807,"date":"2025-06-22T18:50:27","date_gmt":"2025-06-22T18:50:27","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=32807"},"modified":"2025-06-22T18:50:29","modified_gmt":"2025-06-22T18:50:29","slug":"matt-is-five-years-older-than-twice-his-cousin-andys-age","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/matt-is-five-years-older-than-twice-his-cousin-andys-age\/","title":{"rendered":"Matt is five years older than twice his cousin Andy’s age."},"content":{"rendered":"\n

Content = 1.06 Quiz: Inequalities Matt is five years older than twice his cousin Andy’s age. The sum of their ages is less than 35. Let x represent Andy’s age. Which inequality represents Andy’s possible age<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Step 1: Define the variable<\/strong><\/h3>\n\n\n\n

Let:<\/p>\n\n\n\n

    \n
  • xxx = Andy\u2019s age (in years)<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Step 2: Translate the word problem into expressions<\/strong><\/h3>\n\n\n\n

    Matt is five years older<\/strong> than twice<\/strong> Andy\u2019s age.<\/p>\n\n\n\n

    That means Matt\u2019s age can be written as:Matt\u2019s age=2x+5\\text{Matt’s age} = 2x + 5Matt\u2019s age=2x+5<\/p>\n\n\n\n

    The sum<\/strong> of their ages is less than 35<\/strong>, so:x+(2x+5)<35x + (2x + 5) < 35x+(2x+5)<35<\/p>\n\n\n\n

    \n\n\n\n

    Step 3: Simplify the inequality<\/strong><\/h3>\n\n\n\n

    Combine like terms on the left-hand side:3x+5<353x + 5 < 353x+5<35<\/p>\n\n\n\n

    Now subtract 5 from both sides:3x<303x < 303x<30<\/p>\n\n\n\n

    Divide both sides by 3:x<10x < 10x<10<\/p>\n\n\n\n

    \n\n\n\n

    Final Answer:<\/strong><\/h3>\n\n\n\n

    x<10x < 10x<10<\/p>\n\n\n\n

    \n\n\n\n

    Explanation <\/strong><\/h3>\n\n\n\n

    This problem requires interpreting a word problem into a mathematical inequality. It involves relationships between two people\u2019s ages and how their combined ages must remain under a certain value.<\/p>\n\n\n\n

    First, we define the variable xxx to represent Andy\u2019s age. Since Matt is said to be five years older than twice Andy\u2019s age, we represent Matt\u2019s age as 2x+52x + 52x+5. The phrase \u201ctwice Andy\u2019s age\u201d means 2x2x2x, and then \u201cfive years older\u201d means we add 5 to that.<\/p>\n\n\n\n

    Next, we look at the condition that the sum of their ages<\/strong> is less than 35<\/strong>. The sum means we add Andy\u2019s age xxx and Matt\u2019s age 2x+52x + 52x+5. So we form the inequality:x+(2x+5)<35x + (2x + 5) < 35x+(2x+5)<35<\/p>\n\n\n\n

    We combine like terms on the left side to simplify the inequality to 3x+5<353x + 5 < 353x+5<35. Then, we solve it step-by-step by isolating the variable xxx. Subtracting 5 from both sides gives 3x<303x < 303x<30, and dividing both sides by 3 gives the final result x<10x < 10x<10.<\/p>\n\n\n\n

    This inequality shows that Andy\u2019s age must be less than 10 years<\/strong> old for the total of their ages to remain under 35. The solution is both mathematically valid and logically consistent with the original problem.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Content = 1.06 Quiz: Inequalities Matt is five years older than twice his cousin Andy’s age. The sum of their ages is less than 35. Let x represent Andy’s age. Which inequality represents Andy’s possible age The Correct Answer and Explanation is: Step 1: Define the variable Let: Step 2: Translate the word problem into […]<\/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-32807","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32807","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=32807"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32807\/revisions"}],"predecessor-version":[{"id":32809,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32807\/revisions\/32809"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=32807"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=32807"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=32807"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}