Final answer:
After applying a $20 discount to Joseph's total of $410, he has $390 left to spend on pens. At the cost of $7 per pen, he can buy approximately 55 pens.
Step-by-step explanation:
To find out how many pens Joseph can buy with a discount of $20, we need to determine the maximum number of pens he can purchase with his current budget, and then apply the discount. Each pen costs $7, and Joseph has a total of $410. Therefore, we can divide the total amount by the cost of each pen to find out the maximum number of pens he can buy:
Number of pens = Total amount / Cost per pen
In this case, the Number of pens = $410 / $7 = 58.57 (approx.)
Since we can only buy whole numbers of pens, Joseph can buy a maximum of 58 pens. Now, to apply the $20 discount, we subtract $20 from the total amount he has to spend:
Amount after discount = Total amount - Discount
Amount after discount = $410 - $20 = $390
Now, to find out how many pens Joseph can buy with the discounted amount, we divide the new total by the cost per pen:
Number of pens with discount = Amount after discount / Cost per pen
Number of pens with discount = $390 / $7 = 55.71 (approx.)
Again, we can only buy whole numbers of pens, so Joseph can buy a maximum of 55 pens with the discount.