3 Title

Beginning Algebra
Tutorial 16: Percent and Problem Solving

 Answer/Discussion to 1a 82% Dropping the percent sign and then moving the decimal two places to the left we get: 82% = . 82

 Answer/Discussion to 1b 325% Dropping the percent sign and then moving the decimal two places to the left we get: 325% = 3.25

 Answer/Discussion to 2a .64 Moving the decimal place two to the right and then putting a % sign at the end of the number we get: .64 = 64%

 Answer/Discussion to 2b .0003 Moving the decimal place two to the right and then putting a % sign at the end of the number we get: .0003 = .03%

 Answer/Discussion to 3a 54 is 60% of what number?

 Step 1: Understand the problem. Make sure that you read the question carefully several times.  Since we are looking for a number, we will let  x = the number

 Step 2:  Devise a plan (translate).

 Step 3:  Carry out the plan (solve).

 *Inv. of mult. by .60 is div. by .60

 Answer/Discussion to 3b 50.4 is what percent of 120?

 Step 1: Understand the problem. Make sure that you read the question carefully several times.  Since we are looking for a percent, we will let  x = the percent

 Step 2:  Devise a plan (translate).

 Step 3:  Carry out the plan (solve).

 *Inv. of mult. by 120 is div. by 120

 Answer/Discussion to 3c A local furniture store is having a terrific sale.  They are marking down every price 45%.  If the couch you have our eye on was \$800 before the markdown, find the decrease and the sale price.

 Step 1: Understand the problem. Make sure that you read the question carefully several times.  Since we are looking for the decrease in price, we will let  x = the decrease in price

 Step 2:  Devise a plan (translate).

 Step 3:  Carry out the plan (solve).

 *Multiply

 360 is 45% of 800.   FINAL ANSWER:  The decrease is \$360. The sale price is \$800 - \$360 = \$440. (return to problem 3c)

 Answer/Discussion to 4a In 2001, what was the ratio of profit of toilet paper to profit of paper cups?

 When setting up a ratio you need to write the number that corresponds to the first part first and then compare it to the number that corresponds to the second part of the ratio.  What do you think the first part of the ratio, toilet paper or paper cups?  Since toilet paper is listed first, that is what our first number of our ratio has to correspond to.  What is the percentage of profit attached to toilet paper?  Looking on the pie chart, I believe it is 10%. That leaves the percentage associated with paper cups to be our second part of the ratio.  Looks like that will be 15%. So the ratio of profit of toilet paper to profit of paper cups would be 10 to 15.  You can think of ratios as fractions, and simplify them in the same manner.  Since 10 and 15 have a greatest common factor of 5, we can reduce this to be 2 to 3. Note that if you had started with 15 to 10, this would be incorrect.  15 to 10 would be the ratio of profit of paper cups to profit of toilet paper.  You write a ratio, just like you read it, left to right. The simplified ratio of profit of toilet paper to profit of paper cups would be 2 to 3.

 Answer/Discussion to 4b If the profit for napkins in 2001 was 35% lower than its profit in 2000, how much profit was made from napkins in 2000?

 Wow, where do we start?  Since we know the total profit and percent of profit of napkins from 2001, we can start by finding the profit of napkins there was in 2001. What percentage or profit was napkins  in 2001?  If you said 52% you are correct!!! So what would  be the profit of napkins in 2001?  When we take a percentage of a number, we write the percentage in decimal form and then multiply it times the number we are taking the percentage of. Taking 52% of the total profit of 275 million we get: (.52)(275 million) = 143 million 143 million is the profit made on napkins in 2001.     Using this found information we need to find out the profit of napkins in 2000. The question says that the profit for napkins in 2001 was 35% lower than its profit in 2000. We are going to let x be the profit for napkins in 2000 We are needing an equation that represents the English phrase "the profit for napkins in 2001 was 35% lower than its profit in 2000". Going left to right, the profit for napkins in 2001 would be 143 million, was would be our = sign, 35% lower than the its profit in 2000, would be starting with the profit in 2000, which is x and subtracting 35% of that, which is .35x.  From all of this we get the following equation:

 *Subtract like terms *Divide both sides by .65

 The profit that napkins made in 2000 would be \$220 million.

 Answer/Discussion to 4c If the areas of sectors in the circle graphs are drawn in proportion to the percentages shown, what is the measure, in degrees, of the central angle sector representing the percentage of profit of tissues?

 What percentage of the profit in 2001 did tissues make?  If you said 12% you are correct!!! So what would be the measure of the central angle for tissues in 2001?  Keep in mind that a full circle is 360 degrees.  We are basically wanting to know what 12% of 360 degrees is. When we take a percentage of a number, we write the percentage in decimal form and then multiply it times the number we are taking the percentage of. Taking 12% of the total of 360 degrees we get: (.12)(360degrees) = 43.2 degrees The central angle sector for the tissues is 43.2 degrees.

Last revised on July 27, 2011 by Kim Seward.