Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community college charges a $35 registration fee plus $375 per course, what is the greatest number of courses for which Angelica can register? We set up the Tuition function T(c), where c is the number of courses: T(c) = Cost per course * c + Registration Fee T(c) = 35c + 375 The problem asks for the number of courses (c) where her tuition [I]cannot exceed[/I] $1000. The phrase [I]cannot exceed[/I] means less than or equal to, or no more than. So we setup the inequality for T(c) <= 1000 below: 35c + 375 <= 1000 To solve this inequality for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=35c%2B375%3C%3D1000&pl=Solve']type it in our search engine and we get[/URL]: c <= 17.85 Since we cannot have fractional courses, we round down and get: c[B] <= 17[/B]

Anna paints a fence in 4 hours wile her brother paints it in 5 hours. If they work together, how long will it take them to paint the fence? Set up unit rates per hour: [LIST] [*]Anna paints 1/4 of a fence per hour [*]Brother paints 1/5 of a fence per hour [*]Combined, they paint [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Add']1/4 + 1/5[/URL] = 9/20 of a fence per hour [/LIST] Setup a proportion of time to hours where h is the number of hours needed to paint the fence 9/20 of a fence the first hour 18/20 of a fence the second hour 2/20 is left. Each 1/20 of the fence takes 60/9 = 6 & 2/3 minutes 6 & 2/3 minutes * 2 = 13 & 1/3 minutes Final time is: [B]2 hours and 13 & 1/3 minutes[/B]

Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. If they work together, how long will it take them to shovel the sidewalk? Set up unit rates: [LIST] [*]Brandon can shovel 1/8 of a sidewalk per minute [*]His brother can shovel 1/12 of a sidewalk per minute [/LIST] Together, they can shovel: [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F8&frac2=1%2F12&pl=Add']1/8 + 1/12[/URL] = 5/24 of a sidewalk per minute 1 minute = 60 seconds 5/24 / 60 seconds = 1/x seconds 5/24 * 60 = 1/x 5/1440 = 1/x Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5&num2=1&den1=1440&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: x = 288 288/60 = [B]4 minutes and 48 seconds[/B]

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Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LCpl) M and Lance Corporal (LCpl) Z in the ratio 3:5:7. How many rounds did Lance Corporal (LCpl) M receive? Our ratio denominator is: 3 + 5 + 7 = 15 Lance Corporal (LCpl) M gets 5:15 of the ammunition. [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we see that 5/15 = 1/3 So we take 360 rounds of ammunition times 1/3: 360/3 = [B]120[/B]

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When the drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened, it takes 5 hours to empty the pool. The pool is being filled, but the drain was accidentally left open. How long until the pool is completely filled? Set up unit fill rates per hour: [LIST] [*]1/4 of the pool is filled each hour [*]1/5 of the pool is drained away each hour [/LIST] The amount left over after an hour of filling minus draining is: [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Subtract']1/4 - 1/5[/URL] = 1/20 Therefore, it take [B]20 hours to fill the pool[/B]