bkevil Solving Percent Equations Using Proportions Proportion is two equal fractions

bkevil Percent Equations Remember “percent” means:Remember “percent” means: Out of 100 Out of 100 Per 100 Per 100 part of a total of 100 part of a total of 100

bkevil Percent Equations Write every problem, with a percent, in this equation form: percent of total is part 75% x 60 = 45 75% percent x of 60 total = is 45 part

bkevil Percent Equations II. Total is unknown -- “X”“X” 3 kinds of percent equations I. Percent is unknown -- “X”“X” III. Part is unknown -- “X”“X” percent of total is part X X of total is part X percent of X is part percent of total is X

bkevil Percent Equations Write a proportion when percent is missing. I. percent of total is part 75% x 60 = 45 X % percent

bkevil Percent Equations Solve the proportion: 75% x 60 = 45 X % 60 X = 100(45) Cross multiply Solve equation 60 X = 4500 X = 75 X % = 75%

bkevil Percent Equations Write a proportion when total is missing. II. percent of total is part 75% x 60 = 45 X total

bkevil Percent Equations Solve the proportion: 75% x 60 = 45 X 75 X = 100(45) Cross multiply Solve equation 75 X = 4500 X = 60

bkevil Percent Equations Write a proportion when part is missing. III. percent of total is part 75% x 60 = 45 X part

bkevil Percent Equations Solve the proportion: 75% x 60 = 45 X 75 (60) = 100( X ) Cross multiply Solve equation 4500 = 100 X X = 45

bkevil Percent Equations Remember--- IfIf the “” “ X ” is over 100, your answer should have a percent sign “%”. IfIf the “” “ X ” is anywhere else in the proportion, your answer should NOT NOT have a percent sign.

bkevil Example 1– part is missing YouYou plan to buy a radio that costs $ If the local sales tax is 7%, how much must you add to the price of the radio? RewriteRewrite the question as a % equation: What is 7% of 49.99? RewriteRewrite as: percent of total is part 7% x49.99 = X

bkevil Example 1-cont. Solve the proportion: 7% x = 45 X 7 (49.99) = 100( X ) Cross multiply Solve equation = 100 X X = tax= $3.50

bkevil Example 2- total is missing Acompany sent out survey forms to everybody in a particular area. After two weeks, 1450 people had returned their survey forms. If the returned forms represent 18% of the total sent out, how many surveys were sent out? is

bkevil Example 2-cont. RewriteRewrite the question as a % equation: 1450 is 18% of of X ? RewriteRewrite as: as: percent of total is part 1 8% 1 8% x X = 1450 WriteWrite a proportion and solve

bkevil Example 2-cont. Solve the proportion: 18% x X = X = 100(1450) Cross multiply Solve equation 18 X = X = surveys

bkevil Example 3 – % is missing Suppose you must work 40 hours each week to get your full paycheck. This week, you have worked 36 hours. What percent of the requirement have you fulfilled?

bkevil Example 3-cont. Rewrite the question as a % equation:Rewrite the question as a % equation: 36 is % of 40? 36 is X % of 40? Rewrite as: percent of total is partRewrite as: percent of total is part % x 40 = 36 X % x 40 = 36 Write a proportion and solveWrite a proportion and solve

bkevil Example 3-cont. Solve the proportion: X % 40 = X = 100(36) Cross multiply Solve equation 40 X = 3600 X = 90 90% fulfilled

bkevil Simple Interest InterestInterest = Principal x Rate x Time I= prt PrincipalPrincipal is amount of money bowered or invested. RateRate is the percent. Amount (of cents) paid for $1. Must be changed to a decimal. (move the decimal 2 places to the left) TimeTime must be in years!!!!

bkevil Example 4 YouYou put $500 in a savings account. The account pays 4% interest. You leave the money in the account for 6 years. How much interest will you receive? PrincipalPrincipal is the amount of money invested — in this case, $500. RateRate is the percent as a decimal—in this case 4% = TimeTime is years—in this case, 6.

bkevil Example 4- cont. Interest is money paid for the use of money. I = p x r x t formula I = 500 x.04 x 6 substitution I = 120 $120 interest answer labeled

bkevil Example 4 – cont. WhatWhat if you were asked “How “How much money will be in the account at the end of the time period of six years? –Add –Add the principal principal (the amount you put in the account) and the interest (the amount of $ the bank added). –In –In this case, add $500 $500 and $120. Principal + Interest = Total Amount $500 + $120 =$620

bkevil The end