13. If four times the sum of a number and threo is six less than twice the number, what is the number?

let x = the first number

let y = the second number

let z = the third number

The problem starts out with the statement:

"The second of three numbers is six less than twice the first"

Now, let us interpret this sentence one statement at a time:

The second of three numbers:

This is referring to the number which we labelled as "y"

six less than twice the first:

twice the first means the first number, "x", is multiplied by 2

six less means 6 is subtracted from the product

obtaining ---> 2x - 6

the two statements are joined by the word "is" which means "equals to", therefore, we now have:

y = 2x - 6

The second statement reads:

"The third number is four times the first."

Interpreting this sentence, which is made-up of a single statement:

"The third number"

This refers to the one which we labelled as "z"

"four times the first"

meaning 4 times the first number, "x", giving 4x

The two statements are joined by the word "is" which means "equals to," therefore, we now have:

z = 4x

The last statement:

"If the sum of the first and the third is nine more than four times the second"

let us break down this sentence, which is made-up of two statements:

If the sum of the first and the third

"the sum of the first and the third"

meaning x + z

nine more than four times the second

"four times the second" means 4 multiplied by "y" therefore 4y

"nine more" means 9 added to 4y

therefore we now have 4y + 9

the is a word joining these two statements, this is the word "is" which means "equals"

therefore we have

x + z = 4y + 9

Now, we are dealing with this final equation:

x + z = 4y + 9

From the first sentence, it was determined that the "second of three numbers is six less than twice the first" and that equation is:

y = 2x - 6

Substituting this value of "y" into the equation above it yields:

x + z = 4y + 9

x + z = 4 (2x - 6) + 9

x + z = 8x - 24 + 9

x + z = 8x - 15

Our resulting equation is:

x + z = 8x - 15

From the second statement, ""The third number is four times the first," we determined that:

z = 4x

Taking this value of "z" and substituting it into the equation above it yields:

x + z = 8x - 15

x + 4x = 8x - 15

5x = 8x - 15

-3x = -15

x = 5

Therefore, the number for which we are looking is:

x = 5

The value of the second number is therefore:

y = 2x - 6

y = 2 (5) - 6

y = 10 - 6

y = 4

The value of the third number is therefore:

z = 4x

z = 4 ( 5 )

z = 20

I did all the math soo have a great day!.

i dont know i just need points