A baker needs sugar syrup that is 40% sugar. How many gallons of water should he add to 5 gallons of 70% sugar syrup to make the 40% syrup?<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Let’s solve the problem step-by-step:<\/p>\n\n\n\n A baker has 5 gallons<\/strong> of syrup that is 70% sugar<\/strong>. He wants to dilute it with water (which has 0% sugar) to get syrup that is 40% sugar<\/strong>. We need to find out how many gallons of water to add.<\/p>\n\n\n\n Since the syrup is 70% sugar, the amount of sugar in the initial syrup is: sugar amount=5\u00d70.70=3.5 gallons of sugar\\text{sugar amount} = 5 \\times 0.70 = 3.5 \\text{ gallons of sugar}<\/p>\n\n\n\n 5+x gallons5 + x \\text{ gallons}<\/p>\n\n\n\n After dilution, the sugar concentration should be 40%. The amount of sugar remains the same (3.5 gallons), but total volume changes to 5+x5 + x.<\/p>\n\n\n\n So, 3.55+x=0.40\\frac{3.5}{5 + x} = 0.40<\/p>\n\n\n\n Multiply both sides by 5+x5 + x: 3.5=0.40(5+x)3.5 = 0.40 (5 + x)<\/p>\n\n\n\n Distribute 0.40: 3.5=2+0.40×3.5 = 2 + 0.40x<\/p>\n\n\n\n Subtract 2 from both sides: 3.5\u22122=0.40×3.5 – 2 = 0.40x 1.5=0.40×1.5 = 0.40x<\/p>\n\n\n\n Divide both sides by 0.40: x=1.50.40=3.75x = \\frac{1.5}{0.40} = 3.75<\/p>\n\n\n\n The baker needs to add 3.75 gallons of water<\/strong> to the 5 gallons of 70% syrup to get syrup that is 40% sugar.<\/p>\n\n\n\n This problem involves dilution, where a concentrated solution (70% sugar syrup) is mixed with a diluent (water) that contains no sugar to achieve a less concentrated solution (40% sugar syrup). The key is understanding that the total amount of sugar in the solution does not change during the mixing process\u2014only the total volume changes.<\/p>\n\n\n\n Initially, you have 5 gallons of syrup with 70% sugar. Multiplying the volume by concentration gives the total sugar content: 5\u00d70.70=3.55 \\times 0.70 = 3.5 gallons of sugar. When you add water, which contains zero sugar, the sugar content stays at 3.5 gallons but is spread out over a larger volume (the original 5 gallons plus however much water you add, xx gallons).<\/p>\n\n\n\n To achieve a syrup with 40% sugar, the ratio of sugar to total solution must be 0.40. Using the formula: sugar amount=final concentration\u00d7total volume\\text{sugar amount} = \\text{final concentration} \\times \\text{total volume}<\/p>\n\n\n\n and substituting the known sugar amount (3.5 gallons) and volume (5 + xx) gives: 3.5=0.40\u00d7(5+x)3.5 = 0.40 \\times (5 + x)<\/p>\n\n\n\n Solving this for xx, the amount of water to add, results in 3.75 gallons. This means that to lower the sugar concentration from 70% to 40%, the baker must add 3.75 gallons of water to the original 5 gallons of syrup. This process is typical in many practical applications where concentrations need adjustment by dilution.<\/p>\n","protected":false},"excerpt":{"rendered":" A baker needs sugar syrup that is 40% sugar. How many gallons of water should he add to 5 gallons of 70% sugar syrup to make the 40% syrup? The correct answer and explanation is: Let’s solve the problem step-by-step: Problem Restatement: A baker has 5 gallons of syrup that is 70% sugar. He wants […]<\/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-23403","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23403","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=23403"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23403\/revisions"}],"predecessor-version":[{"id":23405,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23403\/revisions\/23405"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=23403"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=23403"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=23403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nProblem Restatement:<\/h3>\n\n\n\n
\n\n\n\nStep 1: Understand what is given<\/h3>\n\n\n\n
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\n\n\n\nStep 2: Calculate the amount of sugar in the initial syrup<\/h3>\n\n\n\n
\n\n\n\nStep 3: After adding xx gallons of water, total volume is:<\/h3>\n\n\n\n
\n\n\n\nStep 4: Set up the equation for final concentration<\/h3>\n\n\n\n
\n\n\n\nStep 5: Solve for xx<\/h3>\n\n\n\n
\n\n\n\nFinal answer:<\/h3>\n\n\n\n
\n\n\n\nExplanation in 300 words:<\/h3>\n\n\n\n