1. Handout Solve the following applications. Draw a table or diagram when necessary.

2. Solving Application Problems. Use ISSUE Use ISSUE I – Identify I – Identify S – Setup S – Setup S – Solve S – Solve U – Understand U – Understand E - Explain E - Explain

3. 1. The sum of two times a number and 7 is 35. What is the number? An equations is made up of two equal expressions. The first step is to find the equal sign. Where is the equal sign in this equation? Now, translate the left and right side of the equal sign.

4. 1. The sum of two times a number and 7 is 35. What is the number? What does sum mean? What does two times a number mean? Is twice the number the same as two times the number? Translate “The sum of two times a number and 7”.

5. 1. The sum of two times a number and 7 is 35. What is the number? 2x + 7 Now, translate the right side of the equal sign. 2x + 7 = 35

6. 1. The sum of two times a number and 7 is 35. What is the number? Solve the equation 2x + 7 = 35 2x + 7 +(-7) = 35 + ( -7) 2x + 7 +(-7) = 35 + ( -7) 2x = 28 2x = 28 x = 14 x = 14 Write the answer in a sentence. The number is 14. The number is 14.

7. 2. 12 less than 5 times a number is 78. What is the number? Solve the equation 5x - 12 = 78 5x - 12 + (12) = 78 + (12) 5x - 12 + (12) = 78 + (12) 5x = 90 5x = 90 x = 18 x = 18 Write the answer in a sentence. The number is 18. The number is 18. (Try this one on your own.)

8. 3. 3 times a number increased by 8 is 62. What is the number? Solve the equation 3x + 8 = 62 3x + 8 + (-8) = 62 + (-8) 3x + 8 + (-8) = 62 + (-8) 3x = 54 3x = 54 x = 18 x = 18 Write the answer in a sentence. The number is 18. The number is 18. (Try this one on your own.) Click Click here to skip this one.

9. 4. One number is 5 more than another. If the sum of the numbers is 55, what are the numbers? Identify the given information. Identify the given information. Set up the equation 1 st num. + 2 nd num = sum Set up the equation 1 st num. + 2 nd num = sum x + x + 5 = 55 x + x + 5 = 55 Solve the equation Solve the equation 2x + 5 = 55 2x + 5 = 55 2x + 5 +(-5) = 55 +(-5) 2x + 5 +(-5) = 55 +(-5) 2x = 50 2x = 50 x = 25 x = 25 1 st number 2 nd number Sum x x + 5 55 X = 25 is one number. What is the second number?

10. 4. One number is 5 more than another. If the sum of the numbers is 55, what are the numbers? x + x + 5 = 55 x + x + 5 = 55 2x + 5 = 55 2x + 5 = 55 2x + 5 +(-5) = 55 +(-5) 2x + 5 +(-5) = 55 +(-5) 2x = 50 2x = 50 x = 25 x = 25 and and x + 5 = 30 x + 5 = 30 1 st number 2 nd number Sum x x + 5 55 The numbers are 25 and 30.

11. 5. One number is 3 times the another. If the sum of the numbers is 64, what are the numbers? Identify the given information. Identify the given information. Set up the equation 1 st num. + 2 nd num = sum Set up the equation 1 st num. + 2 nd num = sum x + 3x = 64 x + 3x = 64 Solve the equation Solve the equation 4x = 64 4x = 64 x = 16 x = 16 1 st number 2 nd number Sum x 3x 64 X = 16 is one number. What is the second number? (Try this one on your own.) The numbers are 16 and 48.

12. 6. John earns $7 an hour less than Mary. Together they earn $33 per hour. How much does each earn? Identify the given information. Identify the given information. Set up the equation John + Mary = sum Set up the equation John + Mary = sum x – 7 + x = 33 x – 7 + x = 33 Solve the equation Solve the equation 2x – 7 = 33 2x – 7 = 33 x = 20 x = 20 John Mary Sum X – 7 X 33 Mary earns $20 per hour. How much does John earn? (REVISED.) John earns $13 per hour and Mary earns $20 per hour.

13. 8. The length of a rectangle is 5 cm more than the width. The perimeter is 98 cm. Find the dimensions of the rectangle? Identify the given information. Identify the given information. Set up the equation 2L + 2W = P Set up the equation 2L + 2W = P 2(x + 5) + 2(x) = 98 2(x + 5) + 2(x) = 98 Solve the equation Solve the equation 2x + 10 + 2x = 98 2x + 10 + 2x = 98 x = 22 x = 22 Length Width Perimeter X + 5 X 98 The width is 22 cm. What is the length? The width is 22 cm and the length is 27 cm.

14. Extra: The sum three consecutive numbers is 87. Find the numbers. Identify the given information. Identify the given information. Set up the equation 1 st + 2 nd + 3 rd = sum Set up the equation 1 st + 2 nd + 3 rd = sum x + (x+1) + (x+2) = 87 Solve the equation Solve the equation 3x + 3 = 87 3x + 3 = 87 x = 28 x = 28 1 st 2 nd 3 rd Sum X X + 1 87 On number is 28. What are the other two? The numbers are 28, 29 and 30 X + 2

15. Extra: The sum three consecutive ODD numbers is 87. Find the numbers. Identify the given information. Identify the given information. Set up the equation 1 st + 2 nd + 3 rd = sum Set up the equation 1 st + 2 nd + 3 rd = sum x + (x+2) + (x+4) = 87 Solve the equation Solve the equation 3x + 6 = 87 3x + 6 = 87 x = 27 x = 27 1 st 2 nd 3 rd Sum X X + 2 87 On number is 27. What are the other two? The numbers are 27, 29 and 31 X + 4

16. Extra: The sum three consecutive EVEN numbers is 204. Find the numbers. Identify the given information. Identify the given information. Set up the equation 1 st + 2 nd + 3 rd = sum Set up the equation 1 st + 2 nd + 3 rd = sum x + (x+2) + (x+4) = 204 Solve the equation Solve the equation 3x + 6 = 204 3x + 6 = 204 x = 66 x = 66 1 st 2 nd 3 rd Sum X X + 2 204 On number is 66. What are the other two? The numbers are 66, 68 and 70. X + 4

17. The end!