james brought a few hamsters. for each day after the first day of the week, the hamsters at 20 grams of food than the previous day. the hamsters grew fast, finishing 1260 grams of food in the first week. how much food did the hamsters eat on the first day?
To find out how much food the hamsters ate on the first day, we need to determine the pattern of food consumption for the rest of the days in the first week.
Let's assume the amount of food they ate on the first day is 'x' grams. According to the given information, the hamsters ate 20 grams more each day after the first day.
So, on the second day, they ate x + 20 grams.
On the third day, they ate (x + 20) + 20 = x + 40 grams.
On the fourth day, they ate (x + 40) + 20 = x + 60 grams.
And so on...
In total, over the span of the first week, the hamsters consumed 1260 grams of food. So, we can write the equation:
x + (x + 20) + (x + 40) + (x + 60) + ... = 1260
Simplifying the equation, we find:
7x + 140 = 1260
Now, we can solve for x:
7x = 1260 - 140
7x = 1120
x = 1120 / 7
x = 160
Therefore, the hamsters ate 160 grams of food on the first day.