7. What amount will reduce the amount due on an invoice of $\$ 9410.25$ by $\$ 842$ if the terms of the invoice are $5 / 10, n / 30$ and the payment was made during the discount period? Approximate to the nearest 100 th.
Solution
Step 1 ：The terms of the invoice '5/10, n/30' mean that a 5% discount is offered if the invoice is paid within 10 days, otherwise the full amount is due within 30 days.
Step 2 ：Since the payment was made during the discount period, the discount can be calculated as follows: \(\text{Discount} = \text{Invoice amount} \times \text{Discount rate} = \$9410.25 \times \frac{5}{100} = \$470.51\)
Step 3 ：The amount that will reduce the amount due on the invoice by \$842 is the sum of the discount and the \$842. So, the payment made = \(\text{Discount} + \$842 = \$470.51 + \$842 = \$1312.51\)
Step 4 ：\(\boxed{\text{Therefore, a payment of approximately \$1312.51 will reduce the amount due on an invoice of \$9410.25 by \$842 if the terms of the invoice are 5/10, n/30 and the payment was made during the discount period.}}\)
