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!.
