{"id":9143,"date":"2017-06-08T03:28:25","date_gmt":"2017-06-08T03:28:25","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=9143"},"modified":"2017-07-31T09:53:13","modified_gmt":"2017-07-31T09:53:13","slug":"math-review-of-digit-and-coin-problems","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-digit-and-coin-problems\/","title":{"rendered":"Math Review of Digit and Coin Problems"},"content":{"rendered":"

Overview<\/h3>\n

Some very common word problems are problems involving digits and problems involving coins.\u00a0 Like motion problems, these word problems can also be solved using equations in two variables.<\/p>\n

Setting up a Digit Problem<\/h3>\n

Any two-digit number can be written as 10x +y where x is the number in the tens column and y is the number in the ones column.\u00a0 Think of expanded notation where a number like 34 can be expressed as 3 times 10 plus 4.\u00a0 The reverse, 43, can be expressed as 4 times 10 plus 3.\u00a0 Common types of digit problems have the sum of the digits equal to a certain number.\u00a0 For example, both 3 + 4 and 4 +3 equal 7.\u00a0 However, if the number 34 is reversed to 43, it is 9 more.<\/p>\n

Solving a Digit Problem<\/h3>\n

Suppose the sum of the digits of a two-digit number is 5.\u00a0 If the digits are reversed, the new number is 27 more than the original number.\u00a0 To set up the problem, find the first equation, x +y =5.\u00a0 If the digits are reversed, 10y +x = 27 +10x +y.\u00a0 Simplify the second equation, so that all the x\u2019s and y\u2019s are on one side of the equation, as 9x-9y =-27.\u00a0 Then there are 2 equations, x +y = 5 and 9x-9y =-27.\u00a0 9(x +y) = 5(9), or 9x +9y = 45.\u00a0 They can then be solved using the addition method, so that 9x +9y =45 + 9x-9y =-27.\u00a0 9x +9x = 18x, 9y-9y cancels out as zero, and 45-27 is 18.\u00a0 18x = 18 means that x equals 1.\u00a0 If x equals 1, then 1 +y = 5, or y equals 4.\u00a0 The original number is 14, and 14 +27 is 41, so the problem checks.<\/p>\n

Setting up a Coin Problem<\/h3>\n

Coin problems are similar to digit problems.\u00a0 There are different types of coins and a total, and that relationship can be expressed with one equation.\u00a0 There are also a number more for one type of coins than another type, and that relationship can be expressed with a second equation.\u00a0 The system of equations can then be solved.<\/p>\n

<\/h3>\n

Solving a Coin Problem<\/h3>\n

Suppose there are 20 coins, some quarters and some dimes.\u00a0 The value of all 20 coins is $3.05.\u00a0 How many quarters and how many dimes are there?\u00a0 Let q equal the number of quarters and d equal the number of dimes.\u00a0 The first equation is q +d = 20.\u00a0 The second equation is 25q +10d = 305.\u00a0 Each quarter is 25 cents and each dime is 10 cents.\u00a0 The number of cents total in $3.05 is 305.\u00a0 The number of dimes can also be expressed in a slightly different form, as d = 20-q.\u00a0 Using the substitution method, 25q +10(20-q) = 305, which can be solved as 25q +200-10q =305, rearranged as (25q-10q) or 15q = 305-200 or 105.\u00a0 If 15q =105, then q equals 7.\u00a0 The number of dimes is 20-7 or 13.\u00a0 To check, 25(7) or 175 plus 10(13) or 130, equals 305.<\/p>\n

<\/h3>\n

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Overview Some very common word problems are problems involving digits and problems involving coins.\u00a0 Like motion problems, these word problems can also be solved using equations in two variables. Setting up a Digit Problem Any two-digit number can be written as 10x +y where x is the number in the tens column and y is […]<\/p>\n","protected":false},"author":22,"featured_media":66894,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[4040,4041,4042],"class_list":["post-9143","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-algebra","tag-solving-digit-problems","tag-solving-word-problems","tag-solving-word-problems-in-two-variables"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/9143","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=9143"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/9143\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media\/66894"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=9143"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=9143"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=9143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}