1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
blondinia [14]
2 years ago
5

How many positive integers less than 1000 are 6 times the sum of their digits ?.

Mathematics
1 answer:
Grace [21]2 years ago
4 0

Only 1, 54.

There are obviously no such 1-digit numbers (1 - 9).

Let n = ab be a 2-digit number whose value is 6 times its digit sum, meaning

n = 10a + b = 6 (a + b)

Then

10a + b = 6a + 6b

4a = 5b

Now, 4 and 5 are coprime, so for equality to hold, a must be a multiple of 5 and b must be a multiple of 4.

The only valid multiple of 5 is 5 itself:

• a = 5   ⇒   5b = 20   ⇒   b = 4

There are 2 multiples of 4 to check. The first one gives the same result as a = 5.

• b = 8   ⇒   4a = 40   ⇒   a = 10

but a must be 1-digit.

So among the 2-digit numbers, only 1 such number exists, n = 54.

Let n = abc be a 3-digit number satisfying the criterion. Then

n = 100a + 10b + c = 6(a + b + c)

100a + 10b + c = 6a + 6b + 6c

94a + 4b = 5c

c must be a number from 1-9, which means at most 5c = 5•9 = 45.

If we take the smallest possible values of a and b, we have

94•1 + 4•0 = 94

but the smallest value of 94a + 4b is larger than the largest value of 5c.

So there are no such 3-digit numbers.

You might be interested in
What is the total price of a $15 meal including 6% sales tax?
aev [14]
15×1.06
=15.9
therefor it is $15.90
4 0
3 years ago
Read 2 more answers
Evaluate each expression. 3^-2
Rus_ich [418]
9 is the answer negatives cancel out creating positve
7 0
3 years ago
Read 2 more answers
Put it in decimal form plssss………
raketka [301]
The answer is 58, because 2/5 is equal to 0.4, and 0.4 multiplied by 145 is 58.
3 0
3 years ago
Read 2 more answers
The total number of calories in a female diet per day should be 1400 calories.
bulgar [2K]

Answer:

420

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
An array of 2 rows of 7 dots has a total of 14 dots. it is called a 2 by __ array​
max2010maxim [7]

It is called a 2 by 7 array.

3 0
3 years ago
Read 2 more answers
Other questions:
  • What is the factoring tree for 27
    12·1 answer
  • Which of the following is the complex conjugate of the complex number below? 4+51i
    10·1 answer
  • Given: f(x) = 1/x+5 and g(x) = x-2.
    7·2 answers
  • Que fracción es equivalente a 5/12
    11·2 answers
  • Find the geometric mean between 4 and 1/4. Show your work.
    6·1 answer
  • What 666.983 divided by 978.087 is?
    7·2 answers
  • A wire of length $100 cm is bent into a rectangle. If the length of the rectangle is $10 cm more than its breadth, find the area
    13·1 answer
  • Use the distributive property to multiply 3(-2m+1)​
    13·1 answer
  • How do I do this???????
    14·1 answer
  • Khali has a box with the dimensions shown. He plans to cover the box with glitter What is the total surface area to be covered w
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!