1. Solve the following word problem. Manny is two years older Enrique. The sum of the their ages is 40. How old is Manny and Enrique? Let: m = Manny’s age e = Enrique’s age m = e + 2 m + e = 40 Solve the system ( e + 2 ) + e = 40 2e + 2 = 40 e = 19 m = e + 2 m = 19 + 2 m = 21 Manny is 21 and Enrique is 19 2e = 38

2. 13.03 Using Systems to solve Word Problems (Perimeter)

3. To solve a word problem using a system: 1) read the problem carefully 2) assign variables and set up a system 3) solve the system 4) answer the question Rectangle Length Width Perimeter P = 2L + 2W

4. Solve the following word problem. The perimeter of a rectangle is 24. The width is 2 more than its length. Find the dimensions of the rectangle. Let: L = length W = width 2L + 2W = 24 W = L + 2 Solve the system 2L + 2(L + 2) = 24 2L + 2L + 4 = 24 L = 5 W = L + 2 W = 5 + 2 W = 7 Length is 5 and Width is 7 4L + 4 = 24 4L = 20

5. Solve the following word problem. The sum of the length and width of a rectangle is 13. The difference of the length and width is 5. Find the perimeter of the rectangle. Let: L = length W = width L + W = 13 L – W = 5 Solve the system 2L = 18 L = 9 L + W = 13 9 + W = 13 W = 4 Perimeter is 26 P = 2L + 2W→ P = 2(9) + 2(4) _____________

6. Solve the following word problem. The sum of the length and width of a rectangle is 14. The length plus twice the width equals 24. Find the perimeter of the rectangle. Let: L = length W = width L + W = 14 L + 2W = 24 Solve the system L + W = 14 W = 10 L + W = 14 L + 10 = 14 L = 4 Perimeter is 28 P = 2L + 2W→ P = 2(4) + 2(10) – L – 2W = – 24 – W = – 10 _______________

7. Solve the following word problem. The perimeter of a rectangle is 16. Three times the length plus five times the width is 34. Find the dimensions of the rectangle. Let: L = length W = width 2L + 2W = 16 3L + 5W = 34 Solve the system 6L + 6W = 48 W = 5 2L + 2W = 16 2L + 2(5) = 16 L = 3 Length is 3 and Width is 5 – 6L – 10W = – 68 – 4W = – 20 2L + 10 = 16 2L = 6 __________________