{"id":19030,"date":"2025-06-13T12:15:32","date_gmt":"2025-06-13T12:15:32","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=19030"},"modified":"2025-06-13T12:15:34","modified_gmt":"2025-06-13T12:15:34","slug":"paul-is-two-years-younger-than-patricia","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/paul-is-two-years-younger-than-patricia\/","title":{"rendered":"Paul is two years younger than Patricia"},"content":{"rendered":"\n<p>Paul is two years younger than Patricia. Daniel is 25% older than Patricia. Ten years ago, Daniel was 50% older than Patricia: How old is Paul currently?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>Let\u2019s solve the problem step-by-step.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Let:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Patricia\u2019s current age = xx<\/li>\n\n\n\n<li>Paul\u2019s current age = x\u22122x &#8211; 2 (since Paul is 2 years younger than Patricia)<\/li>\n\n\n\n<li>Daniel\u2019s current age = x+0.25x=1.25xx + 0.25x = 1.25x (since Daniel is 25% older than Patricia)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Ten years ago:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Patricia\u2019s age = x\u221210x &#8211; 10<\/li>\n\n\n\n<li>Daniel\u2019s age = 1.25x\u2212101.25x &#8211; 10<\/li>\n<\/ul>\n\n\n\n<p>According to the problem:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Ten years ago, Daniel was 50% older than Patricia.<\/p>\n<\/blockquote>\n\n\n\n<p>This means: 1.25x\u221210=1.5(x\u221210)1.25x &#8211; 10 = 1.5(x &#8211; 10)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Solve the equation:<\/h3>\n\n\n\n<p>1.25x\u221210=1.5x\u2212151.25x &#8211; 10 = 1.5x &#8211; 15<\/p>\n\n\n\n<p>Subtract 1.25&#215;1.25x from both sides: \u221210=0.25x\u221215-10 = 0.25x &#8211; 15<\/p>\n\n\n\n<p>Add 15 to both sides: 5=0.25&#215;5 = 0.25x<\/p>\n\n\n\n<p>Divide both sides by 0.25: x=20x = 20<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Now compute Paul\u2019s age:<\/h3>\n\n\n\n<p>Paul=x\u22122=20\u22122=18\\text{Paul} = x &#8211; 2 = 20 &#8211; 2 = \\boxed{18}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer: <strong>Paul is currently 18 years old.<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u270d\ufe0f Explanation (300 words):<\/h3>\n\n\n\n<p>This is a classic algebra word problem involving relationships among three people\u2019s ages. The key is translating words into equations.<\/p>\n\n\n\n<p>First, we let Patricia\u2019s age be the variable xx. Paul is stated to be 2 years younger, so we define Paul\u2019s age as x\u22122x &#8211; 2. Daniel is 25% older than Patricia, which we translate to a multiplier of 1.25. Thus, Daniel\u2019s age becomes 1.25&#215;1.25x.<\/p>\n\n\n\n<p>The crucial piece of information is about their ages <strong>10 years ago<\/strong>: \u201cDaniel was 50% older than Patricia.\u201d To use this, we express both of their ages 10 years ago: Daniel was 1.25x\u2212101.25x &#8211; 10 and Patricia was x\u221210x &#8211; 10. If Daniel was 50% older, that means his age equaled Patricia\u2019s age plus 50% of it \u2014 which is the same as multiplying Patricia\u2019s age by 1.5.<\/p>\n\n\n\n<p>Setting up the equation: 1.25x\u221210=1.5(x\u221210)1.25x &#8211; 10 = 1.5(x &#8211; 10)<\/p>\n\n\n\n<p>We solve it step by step to isolate xx, which gives us Patricia\u2019s age as 20. Using this, we subtract 2 to find Paul\u2019s age: 18.<\/p>\n\n\n\n<p>Always remember to verify the solution using the original statements. Ten years ago, Patricia was 10, Daniel was 15 \u2014 and 15 is exactly 50% more than 10. So the answer holds true.<\/p>\n\n\n\n<p>This systematic approach ensures you solve such age problems accurately.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Paul is two years younger than Patricia. Daniel is 25% older than Patricia. Ten years ago, Daniel was 50% older than Patricia: How old is Paul currently? The correct answer and explanation is: Let\u2019s solve the problem step-by-step. Let: Ten years ago: According to the problem: Ten years ago, Daniel was 50% older than Patricia. [&hellip;]<\/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-19030","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19030","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=19030"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19030\/revisions"}],"predecessor-version":[{"id":19031,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19030\/revisions\/19031"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=19030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=19030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=19030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}