Accelerated Coordinate Algebra Unit 2

Name___________________________  Date_________________ Period________

Lesson 9: Solving Systems Word Problems Guided Notes

Standard and Skills

A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

SWBAT look at a word problem and set up an systems of equations or inequalities in order to solve for the missing variables

Steps to Solving Systems of Equations From Word Problems

Step 1: Define your _________________.

Step 2: Write your____________________.

Step 3: Determine the ______________________ for solving.

Step 4: _______________ for your missing variables.

*Please note: It is always a good idea to check that your answer is correct by plugging it back into the original equations at the end.

Example 1: Write a system of equations and solve using the best method.

The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.

Example 2: Write a system of equations and solve using the best method.

Angela bought shampoo and conditioner on her last trip to Target. The shampoo that she uses costs $5 each while the conditioner she uses costs $7 each. If Angela spent $57 and only ended up with 9 items, how many bottles of shampoo and conditioner did she buy?

Guided Practice

1. Find the value of two numbers if their sum is 12 and their difference is 4.

2. The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

3. The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

Independent Practice

1. Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?

2. There were a total of 480 tickets sold for the school play. Adult tickets sold for $8 and student tickets sold for $5. The ticket sales brought in $3369. How many adult tickets and student tickets were sold?

3. Julie collects dimes and quarters. She has a total of 98 dimes and quarters in a jar. She counted the money and found out she has $14.90 in the jar. How many dimes and quarters does she have?

4. Mrs. Delgado purchased notebooks at 2 for $5.00 and pens at $2 per package. She spent $19.00 for a total of 8 items. How many notebooks and pens did she buy?

5. A school principal ordered 100 pizzas for a total of $1255. Cheese pizzas cost $11.50 each, and pepperoni pizzas cost $13.00 each. How many cheese pizzas and pepperoni pizzas did she ordered?

6. 5 Ms. Hawkinson is planning to take more pictures of her students. She bought 8 rolls of film and 2 camera batteries for $23.00. The next day, she went back and bought 6 more rolls of film and 2 batteries for $18.00. How much did each roll of film and battery cost?

7. The environmental club at Paul sells gum and candy bars as a fundraiser. One afternoon, they sold $200 worth of candy. They need to report how many of each item they sold for their club records. Maura knows that they sold 295 items that day. Candy bars sell for 75 cents and gum sells for 50 cents. How many candy bars and gums did Paul sell?

Homework: Complete on separate piece of paper.

1. Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost of one small box of oranges and one large box of oranges.

2. Two small pitchers and one large pitcher can hold 8 cups of water.  One large pitcher minus one small pitcher constitutes 2 cups of water.  How many cups of water each pitcher can hold?