Please answer! Ignore the work it’s not right

Part A

S = smallest piece

M = medium length piece

L = largest piece

The ratio of the smallest to largest is 2:3, so we can say S = 2x and L = 3x for some positive real number x. The ratio 2x:3x reduces to 2:3.

The third piece (medium length piece) is 1 & 3/4 feet shorter than the longest piece. This means

M = L - (1 & 3/4)

M = L - (1 + 3/4)

M = L - (4/4 + 3/4)

M = L - (7/4)

M = 3x - (7/4)

Add up the three pieces

T = total length

T = S+M+L

T = ( S ) + ( M ) + ( L )

T = ( 2x ) + ( 3x - (7/4) ) + ( 3x )

T = (2x+3x+3x) - 7/4

T = 8x - 7/4

Set this equal to the expression (8/3)x - 7/4 and solve for x

9x - 7/4 = (8/3)x - 7/4

12* [ 8x-7/4 ] = 12*[ (8/3)x - 7/4 ] ... multiply both sides by 12

96x - 21 = 32x - 21

108x = 32x

108x-32x = 0

76x = 0

x = 0/76

x = 0

This is not a useful answer because for example S = 2x = 2*0 = 0, but we can't have a piece of 0 length.

Part B

Instead of (8/3)x - 7/4 feet, we are given a total length of 22 & 1/4 feet.

This is equivalent to the improper fraction 89/4 since

22 & 1/4 = 22 + 1/4

22 & 1/4 = 88/4 + 1/4

22 & 1/4 = 89/4

Let's try to find x now. Set the value of T we got earlier equal to 89/4 and solve for x

T = 8x - 7/4

T = 89/4

8x - 7/4 = 89/4

4*( 8x-7/4) = 4*89/4 multiply both sides by 4 to clear out fractions

32x - 7 = 89

32x = 89+7

32x = 96

x = 3

This is a useful x value because...

S = 2x = 2*3 = 6

M = 3x - 7/4 = 3*3 - 7/4 = 9 - 7/4 = 36/4 - 7/4 = 29/4 = 7 & 1/4

L = 3x = 3*3 = 9

None of the lengths are 0.

Then note how,

T = S+M+L

T = 6 + (7 & 1/4) + 9

T = 6 + (7 + 1/4) + 9

T = (6+9+7) + (1/4)

T = 22 + 1/4

T = 22 & 1/4

Which helps confirm the answers.

There is enough info for her to find the length of each piece in this case. The lengths are

the correct answer is 5 6 and 7