2019 AMC 8 Problems/Problem 1
Contents
Problem 1
Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost
each and soft drinks cost
each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy?
Solution 1
We maximize the number of sandwiches Mike and Ike can buy by finding the lowest multiple of that is less than
This number is
Therefore, they can buy sandwiches for
They spend the remaining money on soft drinks, so they buy
soft drinks.
Combining the items, Mike and Ike buy soft drinks.
The answer is
Solution 2
To double check your work, you can realize that , so
is the largest number of dollars you can spend on sandwiches. Since
, so you have
dollars left.
$\boxed{\textbf{(D) }9}.
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.