Problem of the Day

1. Problem of the Day In a group of 60 triangular and square tiles, 25% are red, and 75% are blue. The ratio of triangles to squares is 1:2. Seventy percent of the squares are blue. Find the number of each kind of tile (red or blue squares or triangles). 3 red triangles, 17 blue triangles, 12 red squares, 28 blue squares

2. Learn to find the percent of a number.

3. Part n Part 67 = Whole Whole 90 100 The human body is made up mostly of water. In fact, about 67% of a person’s total (100%) body weight is water. If Cameron weighs 90 pounds, about how much of his weight is water? Recall that a percent is a part of 100. Since you want to know the part of Cameron’s body that is water, you can set up and solve a proportion to find the answer.

4. Additional Example 1A: Using Proportions to Find Percents of Numbers Find the percent of each number. 30% of 50 30 100 n 50 = Write a proportion. 30 · 50 = 100 · n Set the cross products equal. 1,500 = 100n Multiply. 1,500 100n Divide each side by 100 to isolate the variable. = 100 100 15 = n 30% of 50 is 15.

5. Helpful Hint When solving a problem with a percent greater than 100%, the part will be greater than the whole.

6. Additional Example 1B: Using Proportions to Find Percents of Numbers Find the percent of each number. 200% of 24 200 100 n 24 = Write a proportion. 200 · 24 = 100 · n Set the cross products equal. 4,800 = 100n Multiply. 4,800 Divide each side by 100 to isolate the variable. 100n = 100 100 48 = n 200% of 24 is 48.

7. In addition to using proportions, you can find the percent of a number by using decimal equivalents.

8. Additional Example 2A: Using Decimal Equivalents to Find Percents of Numbers Find the percent of the number. Check whether your answer is reasonable. 9% of 80 Write the percent as a decimal and multiply. 9% of 80 = 0.09 · 80 = 7.2

9. Additional Example 2B: Using Decimal Equivalents to Find Percents of Numbers Find the percent of the number. Estimate to check whether your answer is reasonable. 3% of 12 3% of 12 = 0.03 · 12 Write the percent as a decimal and multiply. = 0.36 Estimate 5% of 12 = 0.6, so 3% of 12 is a little less than 0.6. Thus 0.36 is a reasonable answer.

10. Additional Example 3: Geography Application The estimated world population in 2001 was 6,157 million. About 40% of the people were 19 or younger. What was the approximate number of people 19 or younger, to the nearest million? Find 40% of 6,157 million. 0.40 · 6,157 Write the percent as a decimal. 2,462.8 Multiply. The number of people 19 or younger was about 2,463 million.

11. Lesson Quiz for Student Response Systems 1. Identify 75% of 4. A. 1 B. 2 C. 3 D. 4

12. Lesson Quiz for Student Response Systems 2. Identify 30% of 120. A. 36 B. 38 C. 40 D. 42

13. Lesson Quiz for Student Response Systems 3. Identify 140% of 85. A. 125 B. 120 C. 119 D. 109

14. Lesson Quiz for Student Response Systems 4. Identify 0.6% of 130. A. 0.78 B. 0.80 C. 0.82 D. 0.86

15. Lesson Quiz for Student Response Systems 5. A school has 250 students. If 56% of the students went on a hiking trip, how many students went on a hiking trip? A. 194 students B. 166 students C. 154 students D. 140 students