Percent of Change The percent that a value increases or decreases (Section 5.7 in book) • A percent of change is: – a ratio that compares the change in a quantity to the original amount. • For a percent of change: percent of change amount of change original • amount The percent of change can also be expressed as the equation: amount of change percent of change (original amount) Ex 1) The Mitchell family bought a house several years ago for $120,000. This year, they sold it for $150,000. Find the percent of increase in the price of the house. A percent of increase is a percent of change. Subtract the house values to find the amount of change. Use the starting price as the original amount. percent of change amount of change original amount x $ 150 , 000 $ 120 , 000 100 $ 120 , 000 x $ 30 , 000 100 $ 120 , 000 120 , 000 x 100 ( 30 , 000 ) x 25 % The price of the house increased by 25%. Ex 2) Mercer Middle School had 240 students last year. This year, there are 192 students enrolled. Find the percent of change in the number of students. Is this a percent increase or a percent decrease? The percent of change is a percent of decrease. percent of change Subtract the number of students to find the amount of change. Use the earlier number of students as the original amount. amount of change original amount x 240 192 100 240 x 48 100 240 240 x ( 48 )100 x 20 % The number of students decreased by 20%. Ex 3) A baseball team had 80 players show up for tryouts last year, and this year they had 96 players try out. Find the percent increase in players from last year to this year. percent of change amount of change original x 100 96 80 80 80 x 1600 x 20 % amount The percent of change is a percent of increase. Subtract the number of players to find the amount of change. Use the earlier number of players as the original amount. The number of players trying out increased by 20%. Ex 4) Leo bought a used car for x dollars. One year later, the value of the car was 0.88x. Is this an increase or decrease in value? This shows a decrease in value since 0.88x is less than x, or 1x. How much did the value of the car change? amount of change original new value 1 x 0 . 88 x (1 0 . 88 ) x 0 . 12 x The value of the car decreased by 0.12x. This is a 12% decrease from the original cost.