Problema Solution

James bought a few hamsters. For each day after the first day of the week, the hamsters ate 20 grams of food more than the previous day. The hamsters grew fast, finishing 1260 grams of food in the first week. How much food did the hamster eat on the first day?

Answer provided by our tutors

let


a0 = grams of food the hamster ate on the first day


the hamsters ate 20 grams of food more than the previous day


the second day the hamster ate

a1 = a0 + 20


the third day the hamster ate

a2 = a0 + 20 = a0 + 20 + 20 = a0 + 2*20

.

.

the n-1 day the hamster ate

an = a0 + n*20


at the end of the first week its the 7 th day


the total food the hamster ate is


a0 + a1 + a2 + a3 + a4 + a5 + a6 = 1260


a0 + a0 + 20 + a0 + 2*20 +... + a0 + 6*20 = 1260


7*a0 + 20(1 +2 + ..+ 6) = 1260


7*a0 + 21*20 = 1260


a0 = (1260 - 20*21)/7


a0 = 120 g


the hamster ate 120 grams of food in the first day.