Apiece of wood is cut into three pieces in the ratio 2: 3: 5. if the longest piece is 15 in longer than the shortest piece, find the lengths of the piece of wood.

The required length of the piece of wood is 10;15;20.

Given that,

A piece of wood is cut into three pieces in the ratio of 2:3:5.

If the longest piece is 15 in longer than the shortest piece,

We have to determine,

The lengths of the piece of wood.

According to the question,

A piece of wood is cut into three pieces in the ratio of 2:3:5.

First piece = 2x

Second piece = 3x

Third piece = 5x

Total length of the wood = 2x + 3x + 5x = 10x

If the longest piece is 15 in longer than the shortest piece,

Then, a new length of longest piece = 5x+ 15

Then, The length of the piece of wood is,

First wood = 2x = 2(5) = 10

Second wood = 3x = 3(5) = 15

Third wood = 5x = 5(5) = 25

Hence, The required length of the piece of wood is 10;15;20.

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{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

the correct option is b

step-by-step explanation: