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
Ivahew [28]
3 years ago
8

In the small hamlet of abaze, two base systems are in common use. also, everyone speaks the truth, and no one changes which base

they are using in mid-sentence. one resident said, "26 people use my base, base 10, and only 22 people speak base 14." another said, "of the 25 residents, 13 use both bases and 1 can't use either base." how many residents are there? (use base 10, please!)
Mathematics
2 answers:
meriva3 years ago
8 0
Alright, "<span>of the 25 residents", bingo, we have it, 25
wait, 26 people use my base?, wat

ok, so um

anyway, 13 use both, so 13 of the 26 using base 10 are also in the 22 using base 14
so
26+22-13=35 people using bases
and then there is 1 resident not using anything
35+1=36

36 residents



wait, we had 'of the 25 residents, 13 use both and 1 can't use either'
what happened to the other 11, maybe they are using one or the other?

I say 36 residents
</span>
ollegr [7]3 years ago
8 0

Suppose that the first resident speaks in base $B$. Converting to base $10$, his statement implies that $2B + 6$ people uses base $B$ (notice that base $10$ is actually base $1 \cdot B + 0 = B$), and that $2B+2$ people speak using base $B + 4$. Clearly, the second resident is not talking in base $B$, so he must speak base $B + 4$. Then we can also write all of his statements in terms of the variable $B$. It follows that there are $2(B+4) + 5 = 2B + 13$ total residents, of which $(B+4)+3 = B+7$ are bilingual and $1$ cannot use either base. By the Principle of Inclusion-Exclusion, there are $$(2B + 6) + (2B+2) + 1 - (B+7) = 3B + 2$$total people, and setting this equal to $2B + 13$, it follows that $3B + 2 = 2B + 13 \Longrightarrow B = 11$. Thus, the answer is $2B + 13 = 2 \cdot 11 + 13 = \boxed{35}$.

You might be interested in
Which of the following has a graph that is wider than the graph of y=3x2+2 ? a.y=3x2+3 b.y=0.5x2+1 c.y=4x2 +1 d.y=4x2+1
Goryan [66]
So sorry fir it being this late but the answer is B
5 0
3 years ago
Read 2 more answers
Rose normally pays $118.00 for an airplane ticket to visit her parents. The airline company is offering a 15% discount. How much
maria [59]

Answer:

a

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is the solution to this system of linear equations?
WITCHER [35]

Answer:

(5, -1)

Step-by-step explanation:

x + y = 4

x - y = 6

Add the equations to eliminate y

2x = 10----> x=5

Substitute this value in any equation

5 + y = 4 ----> y = 4-5 ----> y= -1

7 0
4 years ago
Read 2 more answers
7 in. 7 in. 7 in. What is the surface area of a cube that measures 7 inches on each side? square inches​
Vesna [10]
<h3>Answer:   294 square inches</h3>

========================================================

Work shown:

SA = surface area of the cube

SA = 6x^2 .... where x is the side length

SA = 6*7^2 .... replace x with 7

SA = 6*49

SA = 294 square inches

5 0
3 years ago
What is the greatest common factor of 540 and 600
zysi [14]
600= 2x2x2x3x5x5
540=2x2x3x3x3x5 
the common factors are two 2's, one 3 and one 5
2x2x3x5= 60 

gcf of 540 and 600 = 60
5 0
3 years ago
Read 2 more answers
Other questions:
  • A frog is sitting on a stump 4 feet high hops off and lands on the ground.During its leap,the frog's height H in feet is given b
    9·1 answer
  • A machine's efficiency can be greater than 100 percent. <br> a. True <br> b. False
    6·1 answer
  • All 12 12 members of the glee club went to eat at the Hibachi Grill restaurant. The chicken costs $10 $10 per person, while the
    10·1 answer
  • A rectangle has a length of 16 feet and a width of 12 feet. Find the area of the rectangle in square feet.
    11·1 answer
  • Haseem was given the following enlargement. What is the perimeter, in centimeters, of the enlarged triangle?
    6·2 answers
  • I want to plant 45 sunflower plants and 81 rose plants in my garden. If I put the same number of plants in each row and each row
    15·1 answer
  • In 1982, a factory in China could make 15,964 remote controls per day.They packed these controls into boxes for shipping.Each bo
    11·2 answers
  • Clea attends music lessons every 2 weeks, Dane class every 3 weeks, and has a dental appointment every 6 weeks. If she attends a
    14·1 answer
  • True or False? Circle your answer and justify your choice.
    10·1 answer
  • N is an integer.<br><br> write the values of n such that -15&lt;3n≤6
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!