Aboy purchased (bought) a party-length sandwich 54 in. long. he wants to cut it into three pieces so that the middle piece is 6 in. longer than the shortest piece and the shortest piece is 9 in. shorter than the longest piece. how long should the three pieces be?

length of shortest piece = 13 in

length of middle piece =  19 in

length of longest piece =  22 in

Step-by-step explanation:

Total length of sandwich = 54 inch

Let shortest piece = x

Middle piece = x+6

Longest piece = x+9

Add this pieces will make complete sandwich

x+(x+6)+(x+9) = 54

Solving

x+x+6+x+9 = 54

Combining like terms

x+x+x+6+9 = 54

3x + 15 = 54

3x = 54 -15

3x = 39

x = 13

So, length of shortest piece = x = 13 in

length of middle piece = x+6 = 13+6 = 19 in

length of longest piece = x+9 = 13+9 = 22 in

The three pieces should be 13 , 19 , 22 inches

Step-by-step explanation:

* Lets study the information to solve the problem

- The length of the sandwich is 54 in

- The sandwich will cut into three pieces

- The middle piece is 6 inches longer than the shortest piece

- The shortest piece is 9 inches shorter than the longest piece

* Lets change the above statements to equations

∵ The shortest piece is common in the two statements

∴ Let the length of the shortest piece is x ⇒ (1)

∵ The middle piece is 6 inches longer than the shortest piece

∴ The length of the middle piece = x + 6 ⇒ (2)

∵ The shortest piece is 9 inches shorter than the longest piece

∴ The longest piece is 9 inches longer than the shortest piece

∴ The longest piece = x + 9 ⇒ (3)

∵ the length of the three pieces = 54 inches

- Add the length of the three pieces and equate them by 54

∴ Add (1) , (2) , (3)

∴ x + (x + 6) + (x + 9) = 54 ⇒ add the like terms

∴ 3x + 15 = 54 ⇒ subtract 15 from both sides

∴ 3x = 39 ⇒ divide both sides by 3

∴ x = 13

* The length of the shortest piece is 13 inches

∵ The length of the middle piece = x + 6

∴ The length of the middle piece = 13 + 6 = 19 inches

* The length of the middle piece is 19 inches

∵ The length of the longest piece = x + 9

∴ The length of the longest piece = 13 + 9 = 22 inches

* The length of the longest piece is 22 inches

* The lengths of the three pieces are 13 , 19 , 22 inches

answer is x<

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.