1. Writing Systems of Equations

2. The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended? Example 1 Step 1: Assign variables. The question tells you what you are looking for. Adults = a Step 2: Write equations, using your variables, and the information from the paragraph. Should have two equations. $ Eqn: 1.5c + 4a = 5050 Children = c People Eqn: c + a = 2200

3. Example 1 - Continued 1) 1.5c + 4a = 5050 2) c + a = 2200 ● Step 3 : Solve your system for what they are asking for. 1) 1.5c + 4a = 5050 2) -4c – 4a = -8800 - 2.5c = -3750 ● Step 4: Make sure your answers make SENSE! Ex: There CANNOT be 1.5 of a person ! 1500 Children c = 1500 -4( ) -4 -2.5 -2.5 +___________ +

4. Example 1 - Continued 1) 1.5c + 4a = 5050 c = 1500 2) c + a = 2200 1500 + a = 2200 a = 700 -1500 - 1500 700 Adults 1500 Children

5. Brenda and Castel are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. Brenda sold 12 rolls of plain wrapping paper and 11 rolls of shiny wrapping paper for a total of $248. Castel sold 9 rolls of plain wrapping paper and 5 rolls of shiny wrapping paper for a total of $134. What is the cost of one roll of plain wrapping paper? Example 2 Step 1: Assign variables. The question tells you what you are looking for. Cost of 1 roll of shiny = s Step 2: Write equations, using your variables, and the information from the paragraph. Should have two equations. Brenda:12p + 11s = 248 Cost of 1 roll of plain = p Castel: 9p + 5s = 134

6. Example 2 - Continued 1) 12p + 11s = 248 2) 9p + 5s = 134 ● Step 3 : Solve your system for what they are asking for. Only need PLAIN! So eliminate shiny! 1) 60p + 55s = 1240 2) -99p – 55s = -1474 - 39p = -234 ● Step 4: Make sure your answers make SENSE! $6 for cost of plain paper p = 6 -11( ) -11 -39 -39 +_____________ + 5( ) 5

7. Example 3 Step 1: Assign variables. The question tells you what you are looking for. Calls for Mrs. Hooper = h Step 2: Write equations, using your variables, and the information from the paragraph. Should have two equations. Total calls: h + a = 8 Calls for Mr. Anderson = a Hooper: h = a + 2 On the day of the field trip, each teacher must call the parents of any student who has not returned a permission slip. All of Mr. Gomez's students returned their permission slips, so he did not have to make any calls. Mrs. Hooper and Mr. Anderson had to call a total of eight parents. Mrs. Hooper needed to call two more students than Mr. Anderson. How many phone calls did Mr. Anderson make?

8. Example 3 - Continued 1) h + a = 8 2) h = a + 2 ● Step 3 : Solve your system for what they are asking for. a + 2 + a = 8 2a + 2 = 8 2a = 6 ● Step 4: Make sure your answers make SENSE! Mr. Anderson made 3 calls a = 3 2 2 -2 _-2

9. Homework Writing Systems Worksheet