A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
moneybird
 3 years ago
Grade 10 Cayley #25
The digits of the positive integer n include no 9s, exactly four 8s, exactly three 7s, exactly two 6s, and some other digits. If the sum of the digits of n is 104 and the sum of the digits of 2n is 100, then the number of times that the digit 5 occurs in n is...?
moneybird
 3 years ago
Grade 10 Cayley #25 The digits of the positive integer n include no 9s, exactly four 8s, exactly three 7s, exactly two 6s, and some other digits. If the sum of the digits of n is 104 and the sum of the digits of 2n is 100, then the number of times that the digit 5 occurs in n is...?

This Question is Closed

rlsadiz
 3 years ago
Best ResponseYou've already chosen the best response.2for the sake of argument lets assume that all the digits of n from 1> 9 be separated by 0's. i.e. 1020304050606 We know that there are 4 8's, 3 7's 2 6's \[104 = 8(4) + 7(3) + 6(2) +X_{1}\]\[X_{1} = 39\]Where X1 is the sum of the digits less that 6. Notice that \[8 * 2 = 16\]\[1 + 6 = 7\] \[7 * 2 = 14\]\[1 + 4 = 5\] \[6 * 2 = 12\]\[1 + 2 = 3\] \[5 * 2 = 10\]\[1 + 0 = 1\] Since we put a 0 between the digits the double of the number will not "overflow" to the other digits. using or example earlier. Twice of it s 2040608101212. So we could say, \[100 = 7(4) + 5(3) + 3(2) + X_{2}\]\[X_{2} = 51\] Note that lets say i have a number A wherein all its digits are less that 5. The sum of digits of 2A is equal to the double of the sums of digits of A because\[4 * 2 = 8\]\[3 * 2 = 6\]\[2 * 2 = 4\]\[1 * 2 = 2\] So we could say that \[X_{1} = a + 5b\]\[X_{2} = 2a + b\] Where a is the sum of all the digits less than 5 and b is the number of 5's in n. Solving for b \[39 = a + 5b\]\[51 = 2a + b\] \[3 = b\] So the answer is there are 3 5's in n.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.