Question

Your favorite craft store had a weekend sale. On the first day, all $10 items were 70% off. You bought some number of these of these sale items (n) and one $8 item. On the second day, all $10 items were 60% off. You returned and spent the same amount of money as the day before. You purchased a $5 item and an equal number of sale items as the day before (n). How many total sale items did you purchase and how much money did you spend at the craft store during the sale? Part I: Complete the table below to write a system of equations to find the number of sale items purchased and the amount of money spent

Answer 1

For the first day we have the following function:
 f (n) = (0.3 * 10) n + 8
 For the second day we have the following function:
 f (n) = (0.4 * 10) n + 5
 You spent the same amount of money as the day before:
 (0.3 * 10) n + 8 = (0.4 * 10) n + 5
 3n + 8 = 4n + 5
 n = 8-5
 n = 3 items
 We evaluate each function for n = 3
 f (3) = (0.3 * 10) * 3 + 8 = 17 $
 f (3) = (0.4 * 10) * 3 + 5 = 17 $
 The total amount of money is:
 17 + 17 = 34 $
 Answer:
 you purchase 6 items
 you spend at the craft store during the sale $ 34