Difference between revisions of "2019 AMC 8 Problems/Problem 14"
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==Solution 1== | ==Solution 1== | ||
− | Let <math>Day 1</math> to <math>Day 2</math> denote a day where one coupon is redeemed and the day when the second coupon is redeemed. | + | Let <math>\text{Day }1</math> to <math>\text{Day }2</math> denote a day where one coupon is redeemed and the day when the second coupon is redeemed. |
− | If she starts on a <math>Monday</math> she redeems her next coupon on <math>Thursday</math>. | + | If she starts on a <math>\text{Monday}</math> she redeems her next coupon on <math>\text{Thursday}</math>. |
− | <math>Thursday</math> to <math>Sunday</math>. | + | <math>\text{Thursday}</math> to <math>\text{Sunday</math>}. |
− | Thus <math>\boxed{\textbf{(A)}\ Monday}</math> is incorrect. | + | Thus <math>\boxed{\textbf{(A)}\\text{ Monday}}</math> is incorrect. |
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~phoenixfire | ~phoenixfire | ||
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== Solution 2== | == Solution 2== |
Revision as of 19:36, 20 November 2019
Contents
[hide]Problem 14
Isabella has coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupons last, she decides that she will redeem one every days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?
MondayTuesdayWednesdayThursdayFriday
Solution 1
Let to denote a day where one coupon is redeemed and the day when the second coupon is redeemed.
If she starts on a she redeems her next coupon on .
to $\text{Sunday$ (Error compiling LaTeX. Unknown error_msg)}.
Thus is incorrect.
If she starts on a she redeems her next coupon on .
to .
to .
to .
Thus is incorrect.
If she starts on a she redeems her next coupon on .
to .
to .
to .
to .
And on she redeems her last coupon.
No sunday occured thus is correct.
Checking for the other options,
If she starts on a she redeems her next coupon on .
Thus is incorrect.
If she starts on a she redeems her next coupon on .
to .
to .
Checking for the other options gave us negative results, thus the answer is .
~phoenixfire
Solution 2
Let
Which clearly indicates if you start form a you will not get a .
Any other starting value may lead to a .
Which means our answer is .
~phoenixfire
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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.