Step 1: Define the variables<\/h3>\n\n\n\n
Let Each twenty-dollar bill is worth $20, so the value of the bills is: Each quarter is worth $0.25, so the value of the quarters is: The total amount of money is given as $8249.00<\/p>\n\n\n\n We add the value of the twenty-dollar bills and the value of the quarters: Combine like terms: Divide both sides of the equation by 20.75: This result is not a whole number. Since the number of bills and coins must be whole numbers, this suggests that either there is a mistake in the model or a unit mismatch.<\/p>\n\n\n\n Let\u2019s convert all amounts to cents to eliminate decimals.<\/p>\n\n\n\n Twenty-dollar bill = 2000 cents Using the same variables: Now set up the equation: Combine terms: Solve: There are 397 twenty-dollar bills<\/strong> in the cash register.<\/p>\n\n\n\n To solve the problem, we begin by assigning a variable to represent the number of twenty-dollar bills, since that\u2019s one of the unknowns. Let x represent the number of twenty-dollar bills. We\u2019re told that the number of quarters is three times this number, so we represent the number of quarters as 3x. The problem also tells us the total value in the register is $8249.00.<\/p>\n\n\n\n Each twenty-dollar bill is worth $20, and each quarter is worth 25 cents. At first, we try solving using decimal dollars: the value of the bills is 20x dollars, and the value of the quarters is 0.25 multiplied by 3x, which is 0.75x dollars. Adding them gives 20.75x. Setting that equal to 8249 and solving for x gives a non-whole number, which is not valid because we cannot have a fraction of a bill or coin.<\/p>\n\n\n\n To avoid decimal values and get more accurate results, we convert all dollar amounts to cents. Twenty-dollar bills become 2000 cents each, and quarters become 25 cents each. The total value becomes 824900 cents. The value of the twenty-dollar bills is now 2000x, and the value of the quarters is 75x (since 3x quarters at 25 cents each). Adding those gives 2075x, and setting that equal to 824900 results in a simple equation. Dividing both sides by 2075 gives x = 397.<\/p>\n\n\n\n So, the cash register contains 397 twenty-dollar bills.<\/p>\n\n\n\n A cash register contains only quarters and twenty-dollar bills. It contains three times as many quarters as twenty-dollar bills, and the total amount of money in the cash register is $8249.00. How many twenty-dollar bills are in the cash register? The Correct Answer and Explanation is: Step 1: Define the variables Letx = number of […]<\/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-33836","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33836","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=33836"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33836\/revisions"}],"predecessor-version":[{"id":33862,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33836\/revisions\/33862"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=33836"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=33836"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=33836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
x<\/strong> = number of twenty-dollar bills
Since there are three times as many quarters as twenty-dollar bills, the number of quarters is 3x<\/strong><\/p>\n\n\n\nStep 2: Determine the value of the money<\/h3>\n\n\n\n
20 * x = 20x dollars<\/strong><\/p>\n\n\n\n
0.25 * 3x = 0.75x dollars<\/strong><\/p>\n\n\n\nStep 3: Set up the equation<\/h3>\n\n\n\n
20x + 0.75x = 8249<\/strong><\/p>\n\n\n\n
20.75x = 8249<\/strong><\/p>\n\n\n\nStep 4: Solve for x<\/h3>\n\n\n\n
x = 8249 \/ 20.75 = 397.5301\u2026<\/strong><\/p>\n\n\n\nStep 5: Convert to cents<\/h3>\n\n\n\n
Quarter = 25 cents
Total = 824900 cents<\/p>\n\n\n\n
Bills: x<\/strong>
Quarters: 3x<\/strong>
Value from bills: 2000x<\/strong>
Value from quarters: 25 * 3x = 75x<\/strong><\/p>\n\n\n\n
2000x + 75x = 824900<\/strong><\/p>\n\n\n\n
2075x = 824900<\/strong><\/p>\n\n\n\n
x = 824900 \/ 2075 = 397<\/strong><\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
Explanation <\/h3>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"