The second of three numbers is 1 less than the first. The third number is 5 less than the second. The first number is twice as large as the third, find the numbers.

Question

Be sure to include a let statement in your answer.

Answer 1

Let the first number = x, the second = y, and the third = z.

1. y = x - 1
2. z = y - 5
3. x = 2z

Because we cannot solve for an equation with more than one variable, we will need to create a new equation by plugging them into each other Because we know that x = 2z, we can replace the x in the first equation with 2z.

1. y = 2z - 1

We also know that z = y - 5, so we can replace the z in this equation with y - 5.

1. y = 2(y-5) - 1

We now have a equation with one variable and can solve for y. Distribute the 2 to the (y-5) to get rid of the parenthesis and simplify.

1. y = 2y - 10 - 1
2. y = 2y - 11

Now we need to move each y to one side so that we can solve. Adding 11 to both sides and simplify.

1. y + 11 = 2y - 11 + 11
2. y + 11 = 2y

Move the y on the left by subtracting y from both sides and simplify.

1. y - y + 11 = 2y - y
2. 11 = y

Now we know that the second number is 11. Plug this into y = x - 1 and solve. To do this, add 1 to both sides and simplify.

1. 11 = x - 1
2. 11 + 1 = x - 1 + 1
3. 12 = x

Now that we know that x = 12 and y = 11, we just need to find z. Because z = y - 5, we can plug in -11 for y and solve.

1. z = 11 - 5
2. z = 6

That's it! x = 12, y = 11, and z = 6. We can check our answers by plugging these values into our original equations and seeing if they are true.

First equation:

1. y = x - 1
2. 11 = 12 - 1
3. 11 = 11

Second equation:

1. z = y - 5
2. 6 = 11 - 5
3. 6 = 6

Third equation:

1. x = 2z
2. 12 = 2(6)
3. 12 = 12

Answer 2

x=(y-1)

(z-5)=y

2x=z

With no amount; there's nothing more I can tell you.