Question 1099683: Over the last 4 Sundays, I have consumed a total of 32 cinnamon rolls. I ate the most on Sunday number 4, equal amounts Sundays 1 and 3, and the least amount on Sunday number 2. On Sunday number 4, I ate 3 times the number I ate on Sunday 2. On Sunday 1 I ate twice the number of rolls I ate on Sunday number 2. How many cinnamon rolls did I eat on each Sunday?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have:
S1 + S2 + S3 + S4 = 32
you are given that:
the amount you ate on S1 is equal to the amount you ate on S3.
you ate the most on S4.
you ate the least on S2.
the amount you ate on S4 is 3 times the amount you ate on S2.
the amount you ate on S1 is equal to 2 times the amount you ate on S2.
since you ate the least on S2, then let x equal the number of donuts you ate on S2.
since the amount you ate on S4 is 3 times the amount you ate on S2, then let 3x equal the number of donuts you ate on S4.
since the amount you ate on S1 is equal to 2 times the amount you ate on S2, then let 2x equal the number of donuts you ate on S1.
since the amount you ate on S3 is equal to the amount you ate on S1, then let 2x equal the number of donuts you ate on S3.
the amount of donuts you ate on each sunday is represented by.
S1 = 2x
S2 = x
S3 = 2x
S4 = 3x
since the amount you ate on all 4 sundays is equal to 32, you have:
2x + x + 2x + 3x = 32
combine like terms to get 8x = 32
solve for x to get x = 4.
the number of donuts you ate on each sunday is therefore:
S1 = 2x = 8
S2 = x = 4
S3 = 2x = 8
S4 = 3x = 12
for a total of 32.
thaat's your solution.
on S1 you ate 8 and on S2 you ate 4 and on S3 you ate 8 and on S4 you ate 12.
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