{"id":17141,"date":"2025-06-12T09:04:36","date_gmt":"2025-06-12T09:04:36","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=17141"},"modified":"2025-06-12T09:04:40","modified_gmt":"2025-06-12T09:04:40","slug":"a-coin-collector-bought-a-set-of-coins-for-850","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-coin-collector-bought-a-set-of-coins-for-850\/","title":{"rendered":"A coin collector bought a set of coins for 850"},"content":{"rendered":"\n

A coin collector bought a set of coins for 850, making a profit of $50 per coin. how many coins were in the set?<\/p>\n\n\n\n

The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n

Correct Answer: 17 coins<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

We are given:<\/p>\n\n\n\n

    \n
  • The total cost<\/strong> for the set of coins = $850<\/li>\n\n\n\n
  • The profit per coin<\/strong> = $50<\/li>\n<\/ul>\n\n\n\n

    Let\u2019s define the number of coins in the set as x<\/strong>.<\/p>\n\n\n\n

    Since the collector is making $50 profit on each coin<\/strong>, this means the total profit<\/strong> is: Total profit=50\u00d7x\\text{Total profit} = 50 \\times x<\/p>\n\n\n\n

    The total amount the collector sold the coins for<\/strong> (selling price) would be: Selling price=Cost price+Profit=850+50x\\text{Selling price} = \\text{Cost price} + \\text{Profit} = 850 + 50x<\/p>\n\n\n\n

    But we can also express the selling price in terms of price per coin. If there are x<\/strong> coins, the selling price per coin is: Selling price per coin=850+50xx\\text{Selling price per coin} = \\frac{850 + 50x}{x}<\/p>\n\n\n\n

    Alternatively, since he made $50 profit on each coin<\/strong>, the selling price per coin<\/strong> is also equal to the cost per coin plus $50<\/strong>.<\/p>\n\n\n\n

    Let\u2019s calculate the cost per coin<\/strong>: Cost per coin=850x\\text{Cost per coin} = \\frac{850}{x}<\/p>\n\n\n\n

    Therefore: Selling price per coin=850x+50\\text{Selling price per coin} = \\frac{850}{x} + 50<\/p>\n\n\n\n

    Now set both expressions for selling price per coin equal: 850+50xx=850x+50\\frac{850 + 50x}{x} = \\frac{850}{x} + 50<\/p>\n\n\n\n

    Let\u2019s solve this equation: 850+50xx=850x+50\\frac{850 + 50x}{x} = \\frac{850}{x} + 50<\/p>\n\n\n\n

    Multiply both sides by x: 850+50x=850+50×850 + 50x = 850 + 50x<\/p>\n\n\n\n

    This equation simplifies correctly, meaning our logic holds. To find the value of x<\/strong>, we use the total profit approach: 50x=Total profit50x = \\text{Total profit}<\/p>\n\n\n\n

    Now, total selling price = total cost + profit = 850 + 50x
    Let\u2019s try values of x<\/strong> until the total selling price divides evenly:<\/p>\n\n\n\n

    Try x = 17: 50\u00d717=85050 \\times 17 = 850<\/p>\n\n\n\n

    So the profit is $850, and total selling price = 850 + 850 = $1,700<\/strong><\/p>\n\n\n\n

    Now, check: Selling price per coin=170017=100Cost per coin=85017=50\u21d2100\u221250=50 profit per coin\\text{Selling price per coin} = \\frac{1700}{17} = 100 \\text{Cost per coin} = \\frac{850}{17} = 50 \\Rightarrow 100 – 50 = 50 \\text{ profit per coin}<\/p>\n\n\n\n

    \u2705 This matches the condition.
    So, there are 17 coins in the set.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

    A coin collector bought a set of coins for 850, making a profit of $50 per coin. how many coins were in the set? The correct answer and explanation is: Correct Answer: 17 coins Explanation: We are given: Let\u2019s define the number of coins in the set as x. Since the collector is making $50 […]<\/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-17141","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17141","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=17141"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17141\/revisions"}],"predecessor-version":[{"id":17142,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17141\/revisions\/17142"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=17141"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=17141"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=17141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}