Q: Isabella has 6
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 10 days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the 6
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?
Isabella will start off on day x. The days of the week that she redeems the coupons are : x; x + 10; x + 20; x + 30; x + 40; x + 50.
We subtract the greatest multiple of 7 that we can subtract from the list above, because there are 7 days in a week: x, x + 3, x + 6, x + 2, x + 5, x + 1.
If we order them from least to greatest, we get: x, x + 1, x + 2, x + 3, x + 5, x + 6. The only day not represented is x + 4, which we know is Sunday.
If Sunday is x + 4, then we subtract 4 days from it to find the day of the week the first coupon was redeemed on. Sunday - 4 days = Wednesday, making the answer C.
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