Mr.Macho ate 125 hot dogs over a five day period.Each day he ate seven more hot dogs than on the previous day. How many hot dogs did he eat the first day
Recalling the formula for summing 5 terms of an arithmetic sequence,
5/2 (2a+4*7) = 125
solve for a, the first term in the sequence
To find out how many hot dogs Mr. Macho ate on the first day, let's work backwards from the information given.
We know that in total, Mr. Macho ate 125 hot dogs over a five-day period. Let's assume he ate x hot dogs on the first day.
On the second day, he ate 7 more hot dogs than on the previous day, so he ate x + 7 hot dogs.
On the third day, he ate 7 more hot dogs than on the previous day, so he ate (x + 7) + 7 = x + 14 hot dogs.
On the fourth day, he ate 7 more hot dogs than on the previous day, so he ate (x + 14) + 7 = x + 21 hot dogs.
On the fifth and final day, he ate 7 more hot dogs than on the previous day, so he ate (x + 21) + 7 = x + 28 hot dogs.
Adding up the number of hot dogs he ate over the five days:
x + (x + 7) + (x + 14) + (x + 21) + (x + 28) = 125
Simplifying the equation:
5x + 70 = 125
5x = 125 - 70
5x = 55
x = 11
Therefore, Mr. Macho ate 11 hot dogs on the first day.