SOLUTION: Martin ate 100 cookies in five days. Each day he ate 6 more than the day before. How many cookies did he eat on the first day?
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Question 313393: Martin ate 100 cookies in five days. Each day he ate 6 more than the day before. How many cookies did he eat on the first day?
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Martin ate 100 cookies in five days. Each day he ate 6 more than the day before. How many cookies did he eat on the first day?
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Arithmetic series with S(5)=100 and d = 6.
Find a(1)
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Formula: S(n) = a(1)+(n-1)d
100 = a(1) + 4*6
a(1) = 74
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Cheers,
Stan H.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Martin ate 100 cookies in five days. Each day he ate 6 more than the day before. How many cookies did he eat on the first day?
Let the amount of cookies that Martin ate on the 1st day be F
Since he ate 6 more cookies than the previous day, then he would've eaten:
(F + 6) cookies on the 2nd day
F + 6 + 6, or (F + 12) cookies on the 3rd day
F + 12 + 6, or (F + 18) cookies on the 4th day
F + 18 + 6, or (F + 24) cookies on the 5th day
Since he had eaten a total of 100 cookies in 5 days, then we have:
F + (F + 6) + (F + 12) + (F + 18) + (F + 24) = 100
5F + 60 = 100
5F = 40
F = = 8
Therefore, Martin ate cookies on the 1st day.
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Check
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Day 1: 8
Day 2: 8 + 6 = 14
Day 3: 14 + 6 = 20
Day 4: 20 + 6 = 26
Day 5: 26 + 6 = 32
In 5 days, he ate: 8 + 14 + 20 + 26 + 32 = 100
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