We want to find the value of a sum, given that we need to remove some values of that given sum.
We will see that the value of the sum is 6.471
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We start with the sum:
S = 1 + 2 + 3 + ... + 150
And we want to remove all the multiples of 3 and 7.
To do that, we need to find the values of k and c such that
3*k = 150
k = 150/3 = 50
Then we have 50 multiples of 3 in that sum that must be removed.
Now we can do the same for the multiples of 7:
7*c = 150
c = 150/7 = 21.4
Rounding to the next whole number we get 21, meaning that there are 21 multiples of 7 in that sum (where the multiples of 7 and 3 together are counted twice, so we need to add them again)
Then the sum will be:
S = 1 + ... + 150 - 3*(1 + ... + 50) - 7*(1 + ... + 21) + 7*(3 + 6 + 9 + 12 + 15 + 18 + 21)
Now we just need to perform that sum, we will get:
S = 11,325 - 3*1275 - 7*231 + 588 = 6,471
If you want to learn more, you can read:
https://brainly.com/question/11889587
