mr. mancho, my great dane, 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 on the first day
Let X be the number eaten the first day.
X + (X+7) + (X+14) + (X+21) + (X+28) = 125
5X + 70 = 125
5X = 55
X = 11
Check: 11 + 18 + 25 + 32 + 39 = 125
This couls have been obtained more easily (and without algebra) by recognizing that the number consumed on the third day (25) was the average for the five-day period.
eleven
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To determine how many hot dogs Mr. Mancho ate on the first day, we need to consider the pattern mentioned in the question. We know that each day he ate seven more hot dogs than on the previous day.
Let's break down the five-day period:
Day 1: Let's assume Mr. Mancho ate X hot dogs on the first day.
Day 2: On the second day, he ate seven more, so he had eaten X + 7 hot dogs.
Day 3: On the third day, he ate seven more than the previous day, so he had eaten X + 7 + 7 = X + 14 hot dogs.
Day 4: On the fourth day, he ate seven more than the previous day, so he had eaten X + 14 + 7 = X + 21 hot dogs.
Day 5: On the fifth and final day, he ate seven more than the previous day, so he had eaten X + 21 + 7 = X + 28 hot dogs.
We are given that Mr. Mancho ate a total of 125 hot dogs over the five-day period. Thus, we can set up the equation:
X + (X + 7) + (X + 14) + (X + 21) + (X + 28) = 125
By solving this equation, we can determine the value of X, which represents the number of hot dogs Mr. Mancho ate on the first day.