A 29 ft board is cut into three pieces at a sawmill. The second piece is 3 ft longer than the first, and the third piece is 2 ft longer than the second. What are the lengths of the three pieces.

The answer to your question is Piece 1 = 7 ft, Piece 2 = 10 ft, Piece 3 = 12 ft

Step-by-step explanation:

Data

total length = 29 ft

1st piece = x

2nd piece = x + 3

3rd piece = 2nd piece + 2 ft

Process

1.- Write the length of the pieces in terms of x

piece 1 = x

piece 2 = x + 3

piece 3 = (x + 3) + 2

2.- Write an equation to find x

         piece 1 + piece 2 + piece 3 = 29

Substitution

                x  +  x + 3 + (x + 3)  + 2 = 29

Solve for x

               x + x + 3 + x + 3 + 2 = 29

               3x = 29 - 3 - 3 - 2

               3x = 29 - 8

               3x = 21

                 x = 21/3

                 x = 7

3.- Find the length of each piece

Piece 1 = 7 ft

Piece 2 = 7 + 3 = 10 ft

Piece 3 = 7 + 3 + 2 = 12 ft

the length of the first piece is 7ft.

the length of the second piece is 10ft.

the length of the third piece is 12ft.

Step-by-step explanation:

Let x represent the length of the first piece.

Let y represent the length if the second piece.

Let z represent the length if the third piece.

A 29 ft board is cut into three pieces at a sawmill. This means that

x + y + z = 29 - - - - - - - - - - -1

The second piece is 3 ft longer than the first. This means that

x = y - 3

The third piece is 2 ft longer than the second. This means that

z = y + 2

Substituting x = y - 3 and z = y + 2 into equation 1, it becomes

y - 3 + y + y + 2 = 29

y + y + y - 3 + 2 = 29

3y = 29 + 1 = 30

y = 30/3

y = 10

x = y - 3 = 10 - 3

x = 7

z = y + 2 = 10 + 2

z = 12

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

nlgqer

step-by-step