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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation8.14 Percentage Word Problems - 1

 Examples: Cathy and Jill were running for school representative. Cathy received thirty percent of the votes. Jill received four hundred and twenty votes. How many votes were cast in the school, assuming that everybody in the school voted for either Cathy or Jill? Solution: Given: Cathy received 30% of the votes. Jill received four hundred and twenty votes = 420 So, percentage Jill received is 100 - 30 = 70% Let 'x' be the total number of votes cast in the school. Jill received 70% of x which is 420, that can be written in the form of an equation: 70% of x = 420 ----calculating or solving for x 70x/100 = 420 70x = 42000 x = 42000/70 = 4200/7 = 600 In a school play Emma was in charge of selling tickets. Tickets were available for adults and students. Emma reported that 152 more student tickets than adult tickets were sold. 70% of the tickets sold were student tickets. How many student tickets were sold? Solution: Start with the unknown to find that is student tickets, so Let 's' be the student tickets and 'a' be the adult tickets sold. Total tickets sold is s+a 152 more student tickets than adult tickets were sold: s = 152 + a 70% of the tickets sold were student tickets 70% of s+a = s 70(s+a)/100 =s We have 2 unknowns and two equations so solving for s and a we have: s = 152 + a s - 152 = a 70(s+a)/100 =s 70(s+a) = 100s substituting a = s - 150 70s + 70(s-152) = 100s 70s + 70s - 10640= 100s 140s -100s = 10640 40s = 10640 s =10640/40 = 266 Ron earns thirty-four percent on sales of hot dog and twelve percent on sales of soda. This week, he earned \$55.88. His sales of hot dog were \$2 more than his sales of soda. How much did Ron earn by selling hot dogs? Solution: Let 'h' be amount he earned by selling hot dogs and 's' be the by selling soda Sales of hot dogs were \$2 more than his sales of soda h = s + 2 34% hot dog 12% - soda ----------\$55.88 (34/100 x h) + (12/100 x s) = 55.88 34h/100 + 12s/100 =55.88 34h + 12s =8258 substituting h=s+2 34(s+2) + 12s =5588 34s+68 + 12s =5588 34s + 12s =5588 - 68 46s = 5520 s = 5520/46 = 120 h = s + 2 = 120 + 2 = 122 Emma is a real estate agent. Emma just sold a house for her client, Matthew. Matthew paid Emma five percent commission on the selling price. Matthew received \$228,950 after paying the commission for the house. What was the actual selling price of the house? Solution: x - 5% commission = \$228,950 x - 5x/100 =\$228,950 100x - 5x = 22895000 95x = 22895000 x = 22895000/95 = 241,000 Directions: Solve the following word problems. Also write at least ten word problem examples of your own.
 Q 1: The total assets of an individual are worth 1,500,000 dollars. From this, he gave 30% to his wife, 55% to his son, and the remaining to charity. Find the amounts he gave to each.225,000, 825,000, and 450,000 dollars respectively450,000, 825,000, and 225,000 dollars respectively825,000, 225,000, and 450,000 dollars respectively Q 2: The number of color T.V. sets produced in 1987 and 1990 in U.S. were 12 millions and 22 millions respectively. Find the percentage increase in production from 1987 to 1990?83.3%83.9%80% Q 3: A bicycle costs 950 dollars. Its value decreases 5% every year due to usage. What will be its price after a year ?902 dollars902.5 dollars900 dollars Q 4: The population of a country in 1981 was 534 millions. It grew by 23% over the next 10 years. What would be the population in 1991?650.82 millions656 millions656.82 millions Q 5: Number of motor bikes sold in 1986 and 1987 in U.S. were 636,000 and 579,000 respectively. Find the percentage drop in sales in 1987 over 1986?89.6%80%8.96% Q 6: In a class of 60 students, 33 students selected to go to the library and rest of them went to gym. What is the percent of the class that chose to go to gym?55%50%45% Q 7: John earns 3600 dollars per month. He spends 8 1/3% of his income towards house rent and 33 1/3% towards food. Find the amount he spends on rent.500 dollars1200 dollars300 dollars Q 8: kwizNET announced two prizes, namely, 75% of 420 dollars or 35% of 880 dollars for the winner of a math contest. Which prize would you prefer? (hint: select the greater amount)35% of 880 dollars75% of 420 dollars Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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