Mr cruz cut three pieces of wood for a project .the first piece of lumber is the longest. the second is 7/8 times as long as the first piece . the third piece is 12 5/16 inches shorter than the second piece the their piece is 24 7/16 inches long
a)how long is the first piece of wood?
b)how much wood did mr cruz use to make all 3 pieces?
c)mr cruz has 32 ft of lumber left he wants to cut 4 more of each of the pieces described above does he have enough lumber? justify your answer

1st piece is the longest

 2nd piece is 24 7/16 + 12 5/ 16 = 36 3/4 inches long

3rd piece is 24 7/16 inches

 2nd piece is 7/8 as long as first piece so divide the length of the 2nd piece by 7/8

3 3/4 / 7/8 = 42 inches

A) 1st piece is 42" long

 B) now add them all: 42 + 36 3/4 + 24 7/16 = 103 3/16 inches total

C) 103 3/16 inches / 12 = 8.6 feet

8.6 x 4 = 34.4 feet, he has 32 feet so he does not have enough to cut 4 more of each size.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3