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Unit 5 Day 8 Applications of Linear Systems Don’t Let Word Problems Get You Down… Warm Up! Partner Think Tank… How many variables will I need to identify and eventually solve for? a. You decide to order some baseball cards from an online catalogue. Each pack of cards you order costs $3.50, and the shipping fee is a flat $5.00 no matter how many cards you order. If your order came to a total of $50.50, how many packs of cards did you order? b. Suppose you have just enough money, in coins, to pay for a loaf of bread priced at $1.95. You have 12 coins, all quarters and dimes. How many quarters and how many dimes were there? What method would you use to solve a and b? Let’s Practice! The Problem: On Monday, Joe bought 10 bagels and 5 doughnuts for his Algebra I class at the cost of $16.50. It turns out that the doughnuts were more popular than the bagels. On Tuesday he bought 5 bagels and 10 doughnuts for a total of $14.25. What is the price for a bagel and what is the price for a donut? But where do I start? A few helpful hints… Read each word problem at least two to three times. Underline what you know and assign variables to what you need to find. Write equation(s) for the situation: o One equation – you only have one variable to find. Solve using basic algebra. o Two equations (a system) – you have two variables to find; thus, you must write two equations. Solve by graphing (intersection point), elimination or substitution. Determine if your answer is reasonable. Plug your solution back in – does it work?? Let’s solve! Step 1: Identify the variable(s): Step 2: Write your equation(s): Step 3: Solve! Step 4: Check! A few more! Define your variables, set up your system and solve… Example 1: Matt and June are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small boxes of fruit and large boxes of fruit. Matt sold 3 small boxes of fruit and 14 large boxes of fruit for a total of $203. June sold 11 small boxes of fruit and 11 large boxes of fruit for a total of $220. Find the cost each of one small box of fruit and one large box of fruit. Example 2: The Bulls scored a total of 80 points in a basketball game against the Pacers. The Bulls made a total of 37 two point and three point baskets. How many two point shots did the Bulls make? How many 3 point shots did the Bulls make? Example 3: During a football game the parents of the Devils football players sell nachos and popcorn to raise money for new uniforms. They charge $2.50 for nachos, and $2 for a bag of popcorn. The parents collect $336 in sales during the game. They sell a total of 144 items. Set up a system of equations and solve to determine how many nachos and bags of popcorn were sold. Example 4: Find the value of two numbers if their sum is 12 and their difference is 4