5.50 divided by 10 gives you 55. There will be 55 dimes in $5.50 :)
Let's say a = number of ordered soups, b = number of ordered sandwiches.
Then 4.5a + 7.75b = 113.50, and a and b are integers between 0 and 18 inclusive.
How do we tackle this? If all ordered soup, the cost would be $81, so we'll have at least 4 sandwiches. If all ordered sandwich, the cost would be $139.5, so at most 15 sandwiches were ordered. You also know an even number of sandwiches was ordered, to let the price end at 50 cent.
If you brute-force from 4,6,8,10,12 to 14 sandwiches, you find the answer at 10 sandwiches and 8 soups.
10*7.75 + 8*4.50 = 113.50
Simplifying x + 3 + x + 4 = x + 7 + 2x + 7 Reorder the terms: 3 + 4 + x + x = x + 7 + 2x + 7 Combine like terms: 3 + 4 = 7 7 + x + x = x + 7 + 2x + 7 Combine like terms: x + x = 2x 7 + 2x = x + 7 + 2x + 7 Reorder the terms: 7 + 2x = 7 + 7 + x + 2x Combine like terms: 7 + 7 = 14 7 + 2x = 14 + x + 2x Combine like terms: ...
Answer:
The PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5% is $20,352.
Step-by-step explanation:
P = PMT [(1 - (1 / (1 + r)
)) / r]
= 2,700 [(1 - (1 / (1 + 0.055)
)) / 0.05]
= 2,700 [(1 - (1 / (1 + 0.055))) / 0.05]
= 2,700 [(1 - (1 / (1.708)) / 0.05]
= 2,700 [(1 - 0.58)) / 0.05]
= 2,700 [(0.41457) / 0.05]
= 2,700(7.53)
=$ 20,352
