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.