A percent is a value divided by 100. For example, 80% and 45% are equal to 80/100 and 45/100, respectively. Just as a percent is a portion of 100, an unknown is part of a whole.
This article focuses on using percent and proportions to solve for that unknown.
Real Life Example
Leslie and seven of her friends celebrate her birthday at Lindsey Street Grill. The restaurant automatically charges a 20% gratuity. If Leslie’s meal costs $12.00, how much will she need to tip the server?
What do you know?
The tip amount is 20% or 20 percent. Realize that 20 percent means 20 per 100.
20% = 20/100
The meal costs $12.00
With percents, think part/whole.
20 (part)/100 (whole) = x (the part, or the tip, is unknown)/12 (whole)
20/100 = x/12
Cross multiply. Hint: Write these fractions vertically to get the full understanding of cross multiplying. To cross multiply, take the first fraction's numerator and multiply it by the second fraction's denominator. Then take the second fraction's numerator and multiply it by the first fraction's denominator.
20 * 12 = x * 100
240 = 100x
Divide both sides of the equation by 100 to solve for x.
240/100 = 100x/100
2.4 = x
Verify the answer.
Does 20/100 = 2.4/12?
20/100 = .20
2.4/12 = .20
Leslie will tip the server $2.40.
Practice Exercises
A farmer manages a social networking website, farmerandfriends.org, that celebrates backyard gardening. Thanks to the exponential growth of its membership, the website is attracting potential advertisers. The farmer is collecting data on the site’s members so that he can know which advertisers to target.
Here are the solutions and explanations:
1. Farmerandfriends.org discovered that 40% of its members avoid using chemical fertilizers. At the time of the discovery, the site had 120,000 members. How many members avoid using chemical fertilizers? 48,000 members
What do you know?
40 members per 100 avoid chemical fertilizers;
? members per 120,000 avoid chemical fertilizers
40/100 = x/120,000
Cross Multiply.
40 * 120,000 = x * 100
4,800,000 = 100x
Divide both sides of the equation to solve for x.
4,800,000/100 = 100x/100
48,000 = x
Verify the answer.
Does 40/100 = 48,000/120,000
40/100 = .4
48,000/120,000 = .4
2. Farmerandfriends.org learned that members spend $4,250 on gardening conferences. They spend 62.5% of that money on transportation to the convention centers. How much money did these members spend on transportation? $2,656.25
What do you know?
62.5 dollars per 100 are spent on transportation;
? dollars per 4,250 are spent on transportation
62.5/100 = x/4250
Cross Multiply.
62.5 * 4250 = x * 100
265,625 = 100x
Divide both sides of the equation by 100 to solve for x.
265,625/100 = 100x/100
2,656.25 = x
Verify the answer.
Does 62.5/100 = 2,656.25/4250?
62.5/100 = .625
2,656.25/4250 = .625
3. Farmerandfriends.org studied the members who are fans of the Lasagna Gardening page. Of the 2,275 fans, 20% practice Lasagna Gardening.
A. How many fans of the fan page actually practice Lasagna Gardening? 455 fans
What do you know?
20 fans per 100 practice Lasagna Gardening;
? fans per 2,275 practice Lasagna Gardening
20/100 = x/2,275
Cross Multiply.
20 * 2,275 = x * 100
45,500 = 100x
Divide both sides by 100 to solve for x.
45,500/100 = 100x/100
455 fans = x
Verify the answer.
Does 20/100 = 455/2,275?
20/100 = .2
455/2,275 = .2
B. How many fans don’t practice Lasagna Gardening? 1,820 fans
2,275 fans – 455 fans = 1,820 fans
4. On farmerandfriends.org, 6,400 members grow tomatoes. Of these tomato gardeners, 25% sell their tomatoes at the local farmers markets. How many sell their tomatoes at the farmers markets? 1,600 tomato gardeners
What do you know?
25 tomato gardeners per 100 sell their tomatoes at the farmers markets;
? tomato gardeners of 6,400 sell their tomatoes at the farmers markets
25/100 = x/6,400
Cross Multiply.
25 * 6,400 = x * 100
160,000 = 100x
Divide both sides by 100 to solve for x.
160,000/100 = 100x/100
1,600 = x
Verify the answer.
Does 25/100 = 1,600/6,400?
25/100 = .25
1,600/6,400 = .25
5. Farmerandfriends.org, a social networking site, boasts 120,000 members. Of those members, 75 percent buys gardening books.
A. How many members buy gardening books? 90,000 members
What do you know?
75 members of 100 buy gardening books;
? members of 120,000 buy gardening books
75/100 = x/120,000
Cross Multiply.
75 * 120,000 = x * 100
9,000,000 = 100x
Divide both sides of the equation by 100 to solve for x.
9,000,000/100 = 100x/100
90,000 = x
Verify the answer.
Does 75/100 = 90,000/120,000?
75/100 = .75
90,000/120,000 = .75
B. How many members don’t buy gardening books? 30,000 members
120,000 members – 90,000 members = 30,000 members