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Math · Advanced Math
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Systems of Equations and Inequalities Unit Portfolio ALGEBRA 1 A Directions: Complete each of the tasks outined be ow Task 1 You are starting a new business in which you have decided to sell two products instead of just one Determine a business you could start and choose two products that you could se How much of your own money are you willing to invest in this business in order to get started? How much wi each item cost you to make? How much will you charge for each item? Explain this business (how much of your own money youre wi ing to spend on the business, what items youre going to setl, costs for each item, sale price for each item, etc ) a b Consider the total amount youre willing to spend on the business and how much it will cost you to make your items Write an inequality that represents the fact that while making each item, you cant exceed this limit Be sure to include the cost per item in this inequa lity Graph your inequality Be sure to label your graph and shade the appropriate side of the line c d Choose a point that falls in the shaded region Explain what the x coordinate and y coordinate represent and the significance in terms of cost of this point fal ling in the shaded region Choose a point that fals direct y on the line Explain what the x coordinate and y coordinate represent and the significance in terms of cost of this point fall ing direct y on the line e f Choose a point that does not fall in the shaded region Explain what the x this point faling outside of the shaded region

Task 2 Consider the tota amount youre wi ing to spend to start your business After se ing your items, you want your tota amount earned to be at east three times the amount you origina y spent a How much money are you hoping to earn from se ing your products? b Determine the price you want to se each item for Note:You may need to adjust the origina prices that you came up with in Task1 Write an inequa ity that represents the fact that you want your tota earned to be at east three times the amount that you origina y spent Be sure to inc ude the price for each item in this inequa ity Graph your inequa ity Be sure to abe your graph and shade the appropriate side of the ine In the context of the prob em, does the shaded area make sense? If not, make sure to adjust the origina va ues (the investment and the sa e price for both products) so that your shaded area is reasonab e Choose a point that fa s in the shaded region for both this inequa ity and the inequa ity you found in Task 1 Exp ain what the x coordinate and y coordinate represent and the significance in terms of both cost and money earned of this point fa ing in the shaded regions What is the idea number of items you shou d produce and se ? Why? c d f Task 3 Pick one of your items You have been contacted by a customer in A aska who wants to purchase severa of these items and wants you to ship the items to her You have a ready estab ished the cost per item and you wi customer $5 to ship these items to A aska Suppose another company se s the same item but charges ha f of your price However, if the customer buys from this company, she wi be charged $20 in shipping costs on y charge the Write two equations to represent the customers tota cost based on how many items she buys from each of the two se ers you and the other company If the customer in A aska wants to buy 5 items, from whom shou d she buy? Exp ain your answer a b c If the customer in A aska wants to buy 50 items, from whom shoud she buy? d So ve the system of equations from part A What method did you choose to e Exp ain what your so ution for part D means in terms of the situation Exp ain your answer so ve the system? Why?



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