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theangelsanchez
13.12.2021 •
Mathematics
Cassandra categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The percentages she spent in each category are pictured below.
Rent
29%
Food
23%
Fun
19%
Other
29%
If Cassandra spent a total of $2300 this month, how much did she spend on Fun?
Solved
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Ответ:
16
Step-by-step explanation:
We must find integers x, y with the most amount of prime divisors, not necessarily distinct, such that x + 3y < 1,000.
Obviously, this is achieved when the divisor is the least prime 2. So, we must find integers n, m such that
since
, then n must be 9. For n=9 we find the greatest integer m such that
and we find m=7
and
,
are the numbers we are looking for and the sum of their length is 9+7 = 16.
So, 16 is the maximum possible sum of the length of x and the length of y.