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How Do You Figure Out a Percent of Change?

Mr. Lewis decided it was time to sell his car. He originally bought the car for $12,100. After he bought it he put some work into the car, including adding gold-plated rims engraved with "Algebra Rules!" Because of this, he sold his car to an algebra teacher for $13,552. What was the percent of increase in the price of the car?

Summary

  1. 'c' is a variable that represents the percent of increase in the price of the car
  2. The amount of change is the difference between the new price, 13,552, and the original price, 12,100, which is 1,452
  3. The original amount was 12,100
  4. The percent of change is c, our unknown
  5. Multiply 12,100•c on the left
  6. Multiply 1,452•100 on the right
  7. 1,452•100=145,200
  8. 145,200/12,100=12

Notes

    1. We're trying to find the percent the price of Mr. Lewis's car increased by
    1. 'c' is a variable that will represent the percent of increase in the price of the car
    1. The amount of change is the difference between the original amount and the new amount
    1. Setting these two ratios equal to each other gives us a proportion we can solve for percent of change
    1. We need to look back at our problem and pick out what we already know
    1. The amount of change is the difference between the original amount and the new amount
    1. The amount of change is the difference between the original amount and the new amount
    2. Since we're just looking at the size of the change, it doesn't matter whether it's positive or negative
    3. So we can take the absolute value of the new amount, $13,522, minus the old amount, $12,100
    1. The vertical bars mean we are taking the absolute value
    2. We are finding a difference, so we need to subtract
    3. The absolute value means we will take whatever is inside the vertical bars and make the value positive
    4. When we subtract we get a positive value, 1,452
    5. So when we take its absolute value, it stays positive
    6. So 1,452 is our amount of change
    1. 'c' is a variable that represents the percent of increase in the price of the car
    2. This is our unknown that we will be solving for
    1. We have 1,452/12,100 on the left hand side of our proportion
    1. We have c/100 on the right hand side of our proportion
    1. 'c' is a variable that represents the percent of increase in the price of the car
    2. We can use the means extremes property of proportions to cross multiply and find c
    1. 'c' is a variable that represents the percent of increase in the price of the car
    2. We can cross multiply to get an equation we can solve for c
    1. Multiply the means, 12,100 and c, to get the left hand side of the equation
    2. Multiply the extremes, 1,452 and 100, to get the right hand side of the equation
    3. 'c' is a variable that represents the percent of increase in the price of the car
    1. This gives us 12,100c=145,200
    2. 'c' is a variable that represents the percent of increase in the price of the car
    1. Division is the opposite of multiplication
    2. So to get rid of the 12,100, we need to divide by 12,100 on both sides
    3. On the left, the 12,100's cancel out to leave us with c
    4. On the right, 145,200/12,000=12
    1. 'c' is a variable that represents the percent of increase in the price of the car
    1. 'c' is a variable that represents the percent of increase in the price of the car
    2. A percent sign looks like this: %
    1. Since the price of the car increased, we have a percent of increase