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Mathematical Problem Sets for Everyday Scenarios

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    Mathematical Problem Sets for Everyday Scenarios Performance model 1. If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes? A : The following proportion may be written: 1/p=x/5. Solving for the variable, x, gives xp = 5, where x=5/p. So, Lynn can type 5/p pages, in 5 minutes. A. 5/p 2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? A. 2 hours and 24 minutes 2. A: Sally can paint 1/4 of the house in 1 hour. John can paint 1/6 of the same house in 1 hour. In order to determine how long it will take them to paint the house, when working together, the following equation may be written: 1/4 x+1/6 x=1. Solving for x gives 5/12 x=1, where x = 2.4 hours, or 2 hours, 24 minutes. 1 + 1= 2 4 * 6=24/2=12*2=24 3. Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450? D: Sale Price = $450 - 0.15($450) = $382.50, Employee Price = $382.50 - 0.2($382.50) = $306 450*.15=67.50 382.50*.20=76.50 =306. 4. The sales price of a car is $12,590, which is 20% off the original price. What is the original price? (Original Price) = 0.8(Original Price), Original Price = $12,590/0.8 = $15,737.50 D. $15,737.50 5. Solve the following equation for A : 2A/3 = 8 + 4A A: In order to solve for A, both sides of the equation may first be multiplied by 3. This is written as 3(2A/3)=3(8+4A) or 2A=24+12A. Subtraction of 12A from both sides of the equation gives - 10A=24. Division by - 10 gives A = - 2.4. A. - 2.4 6. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue? A. 8 7. Alfred wants to invest $4,000 at 6% simple interest rate for 5 years. How much interest will he receive? E. $1,200

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    8. Jim is able to sell a hand - carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him? 8. A: $670 = Cost + 0.35(Cost) = 1.35(Cost), Cost = $670/1.35 = A. $496.30 9. The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel room that costs $55 before taxes, how much will the city receive in taxes from him? The amount of taxes is equal to $55*0.003, or $0.165. Rounding to the nearest cent gives 17 cents. D. 17 cents 10. A student receives his grade report from a local community college, but the GPA is smudged. He took the following classes: a 2 hour credit art, a 3 hour credit history, a 4 hour credit science course, a 3 hour credit mathematics course, and a 1 hour science lab. He received a "B" in the art class, an "A" in the history class, a "C" in the science class, a "B" in the mathematics class, and an "A" in the science lab. What was his GPA if the letter grades are based on a 4 point scale? (A=4, B=3, C=2, D=1, F=0) C: The GPA may be calculated by writing the expression, ((3*2)+(4*3)+(2*4)+(3*3)+(4*1))/13, which equals 3, or 3.0. C. 3.0 11. Simon arrived at work at 8:15 A.M. and left work at 10: 30 P.M. If Simon gets paid by the hour at a rate of $10 and time and ½ for any hours worked over 8 in a day. How much did Simon get paid? C: From 8:15 A.M. to 4:15 P.M., he gets paid $10 per hour, with the total amount paid represented by the equation, $10*8=$80. From 4:15 P.M. to 10:30 P.M., he gets paid $15 per hour, with the total amount paid represented by the equation, $15*6.25=$93.75. The sum of $80 and $93.75 is $173.75, so he was paid $173.75 for 14.25 hours of work. C. $173.75 12. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? D: If she removes 13 jellybeans from her pocket, she will have 3 jellybeans left, with each color represented. If she removes only 12 jellybeans, green or blue may not be represented. D. 13 13. If r = 5 z then 15 z = 3 y, then r = A: The value of z may be determined by dividing both sides of the equation, r=5z, by 5. Doing so gives r/5=z. Substituting r/5 for the variable, z, in the equation, 15z=3y, gives 15(r/5)=3y. Solving for y gives r = y. A. y

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