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
Andrew deposits $300 into an account that earns 2% interest each year. After the first year, Andrew has $306 in the account. Aft
Sliva [168]

Answer:

It is a simple interest account

Step-by-step explanation:

As we might see from the given earnings, the amount of money he earned each year is the same as in the previous year. This means that the amount of money is growing linearly instead of exponentialy. This is characteristic to a simple interest account, which is found by using the formula:

I=Prt

where I = interest earned.

P = principal

r = Interest rate

t = time in years,

if we use this formula to calculate the amount of money earned after t years, we can see it will be the same as the values reported:

I=$300(0.02/year)(1year)=$6

I=$300(0.02/year)(2years)=$12

I=$300(0.02/year)(3years)=$18

So this simple interest account.

8 0
3 years ago
Plssss do this!!!!! thanks
lisabon 2012 [21]

Answer:

4) SU = TU                    definition of a midpoint

5) ΔSVU ≅ ΔTWU        Side-Side-Side

6) ∠SVU ≅ ∠TWU        corresponding parts of congruent triangles are congruent

Step-by-step explanation:

7 0
3 years ago
Can i get some help please??? Thanks!!!!
Musya8 [376]

Answer: try 34

Step-by-step explanation:

8 0
3 years ago
How much do 1.5 pounds of Havarti cheese cost?
monitta

Answer:

g

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
8,595 ÷ 24 answer please
MatroZZZ [7]

Answer:

358.125

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Other questions:
  • Which of the following statements are not proportional 4/6=9/12 2/3=12/18 5/4=10/8 7/5=36/25
    15·2 answers
  • A 12 sided die is rolled. The set of equally likely outcomes(1,2,3,4,5,6,7,8,9,10,11,12).Find the probability of rolling a 7
    11·1 answer
  • Marilyn has two credit cards, D and E. Card D has a balance of $691.64, and Card E has a balance of $1,014.22. The minimum month
    5·2 answers
  • Ginny has 3 pink tops 4 blue tops and 7 black tops. She has 5 black pants 4pairs of blue jeans and 2 pair of red pants. How many
    7·1 answer
  • Aiden has a collection of 63 nickels and quarters in his piggy bank. If the total value of the coins is $10.75, how many nickels
    15·1 answer
  • A function of the form f(x) ott is modified so that the b value remains the same but the a value is increased by 2. How do
    13·2 answers
  • Rebecca wants to buy a bracelet that is $69.99 but today she can buy it for 20% off the price. What is the amount she will save?
    12·1 answer
  • This 2 pls i need help with explanation sum
    9·1 answer
  • HELP Two workers, if they were working together, could finish a certain job in 24 days. If one of the workers does the first hal
    10·1 answer
  • Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extra
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!