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
Leto [7]
3 years ago
7

In a set of five consecutive integers, the smallest integer is more than 2/3 the largest. What is the smallest possible value of

the sum of the five integers?
Mathematics
2 answers:
astraxan [27]3 years ago
4 0
The answer is: "55".
________________
"55" is the smallest possible value of the sum of the five integers.
________________________________________
We are given five (5) consecutive integers.
___________________________________
Let us represent the first integer as: "x"; 
___________________________________
The second integer as: "x + 1" ; 
___________________________________
The third integer as: "x + 2" ; 
___________________________________
The fourth integer as: "x + 3" ; 
___________________________________
The fifth integer as: "x + 4" ; 
___________________________________
We are given: The smallest integer is MORE THAN (⅔ of the largest integer.
____________________________________
The smallest integer, "x" is greater than: "(⅔) (x + 4)"
________________________________________________
Note the distributive property of multiplication:
__________________________________
→  a*(b + c) = ab + ac ;
__________________________________
→ As such; (⅔) (x + 4) = [(⅔)*(x)] + [⅔)*(4); 
________________________________________
→ (⅔) (x + 4) = [(⅔)*(x)] + [⅔)*(\frac{4}{1})
______________________________________________
{Note: [⅔)*(\frac{4}{1})=\frac{2*4}{3*1}=\frac{8}{3}}; 
_______________________________________________
→ Rewrite the equation: → ⅔ of the largest integer =
______________________
→ (⅔) *(x + 4) = (⅔)x + \frac{8}{3} ;
_______________________________
The smallest, "x", is GREATER than: (⅔)x + \frac{8}{3} ; 
________________________________
→ Write as:  x > (⅔)x + \frac{8}{3}
______________________________________
→ Multiply the ENTIRE "inequality" (BOTH SIDES) by "3", to get rid of the "fractions":
_______________________________
3*{  x > (⅔)x + \frac{8}{3} } ; to get: 
________________________________________
→ 3x > 2x + 8 ; → Now, subtract "2x" from EACH SIDE of the inequality;
_________________________
 → 3x − 2x > 2x + 8 − 2x ;  
______________________
→ to get:  →  x > 8
____________________
Now, we want to to know the "smallest possible value of the sum five          integers".
___________________________________
→That is, the smallest possible value of the sum of :
___________________________________________
→x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 5x + 10.
__________________
So, we want to know the smallest value of "(5x + 10)" ; x > 8, 
_______________________________________________
→ Let us solve for "5x + 10" ; when x = 10; by substituting "8" for "x"
________________
→ 5x + 10 = (5*8) + 10 = 40 + 10 = 50
___________________________________
So, if "x > 8"; then "x" must be greater than "8"; 
_____________________________
When "x = 8", the sum of the 5 (five) integers in our problem = 50.
___________________________
Since "x" in the first of the consecutive integers in the problem; we know that "x > 8"; then the smallest possible value for "x" would be "9"; since "x" has to be an integer.
______________________________
So, we know that:
The smallest possible value of sum of the value integers =
 5x + 10; when x = 9; 
_________________
→ So, we plug "9" for the value of "x" and solve:
______________________________
→ 5(9) + 10 = 45 + 10 = 55 ; → which is our answer.
_____________________________________
Let us check our answer:
_______________________
→ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = ? 55?
                                                           (when "x = 9" ?)?? ;
___________________________________________________
→  9 + (9 + 1) + (9 + 2) + (9 + 3) + (9 + 4) = ? 55? ;
______________________________________
→  9  + 10 +  11 + 12 + 13 = ? 55 ?? ;  Yes!.
__________________________________________
Also, is the answer: 55 , Reasonable? Yes, since it is an integer, and 5 consecutive integers added together would "add up" to an integer value.
__________________________________________
Hope this answer and lengthy explanation is helpful.
Best of luck!
_______________________
Natali [406]3 years ago
3 0

Answer:

55

Step-by-step explanation:

You might be interested in
9 weeks and 5 days<br> - 1 week and 6 days<br> ------------------------------
Butoxors [25]

Answer:

55 days or about 7 weeks

Step-by-step explanation:

9(7)= 63              because there are 7 days in one week

63+5=<u><em>68</em></u>

1(7)=7

7+6=<u><em>13</em></u>

68-13=55

6 0
3 years ago
Read 2 more answers
What are characteristics of nonvascular plants? (Select all that apply.)
igomit [66]

Answer: They have xylem vessels and phloem vessels

Step-by-step explanation:

7 0
2 years ago
Find the slope of the line shown on the graph. Please help! :(
Anna [14]

Answer:

It's really easy just remember rise over run.

Step-by-step explanation:

so you rise 3 and run to the right 3

A great tip that helps me determine if it's positive or neagitve is if you go to the left then it's ALWAYS neagtive but if you go to the right then it's ALWAYS postive

7 0
3 years ago
Read 2 more answers
Square root of 75 plus square root of 3
olya-2409 [2.1K]
Answer:
6√3

Explanation:
Before we begin, remember the following:
\sqrt{a*b} = \sqrt{a}  *  \sqrt{b}
m \sqrt{a} + n \sqrt{a}  = (m+n) \sqrt{a}

Now, for the given:
75 can be written as 25*3
This means that:
\sqrt{75} = \sqrt{25*3}
Applying the above concept, we can find that:
\sqrt{75} = \sqrt{25*3} = \sqrt{25}  *  \sqrt{3}
Now, we know that:
√25 = 5 (we ignored the negative value)

This means that:
√75 = 5√3

Finally, we can compute the needed sum as follows:
√75 + √3 = 5√3 + √3 = 6√3

Hope this helps :)

8 0
3 years ago
Read 2 more answers
Is –54 ÷ 6 positive or negative?
Zigmanuir [339]

Answer:

Negative

Step-by-step explanation:

  1. –54 ÷ 6 = -9

7 0
3 years ago
Other questions:
  • you invest 1,600 calculate the balance of your account after 6 years. round your answer to the nearest hundredth
    11·1 answer
  • 2.2
    6·1 answer
  • Can you explain these words Rate, Per, Divide, Unit and the connections you see between them. Thank you very kind!!!
    7·1 answer
  • What is -7 divided by 1/2?
    10·2 answers
  • The diameter of a circle of 255 π is:
    10·1 answer
  • What is the product in lowest terms?
    10·2 answers
  • ‼️‼️help please ASAP
    11·1 answer
  • Dora irons and annual salary of $85,608 how much does she earn every month
    13·2 answers
  • A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fai
    11·1 answer
  • Find the value of y.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!