Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation 8.14 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.