QuestionFind three numbers where their sum is 86, the second is 9 less than the first, and the third is 3 times the first.

Studdy Solution

STEP 1

Assumptions1. The sum of three numbers is86. The second number is9 less than the first number3. The third number is3 times the first number

STEP 2

Let's denote the first number as $x$ , the second number as $y$ , and the third number as $z$ . We can write the given conditions as equations1. $x + y + z =86$
2. $y = x -9$ . $z =x$

STEP 3

Now, we can substitute the expressions for $y$ and $z$ from the second and third equations into the first equation.
$x + (x -9) +3x =86$

STEP 4

implify the equation by combining like terms.
$x -9 =86$

STEP 5

Add9 to both sides of the equation to isolate the term with $x$ .
$5x =86 +9$

STEP 6

implify the right side of the equation.
$5x =95$

STEP 7

Divide both sides of the equation by5 to solve for $x$ .
$x = \frac{95}{5}$

STEP 8

Calculate the value of $x$ .
$x = \frac{95}{5} =19$

STEP 9

Now that we have the value of $x$ , we can find the values of $y$ and $z$ by substituting $x =19$ into the equations $y = x -9$ and $z =3x$ .
For $y$ , we have $y = x -9 =19 -9$

STEP 10

Calculate the value of $y$ .
$y =19 -9 =10$

STEP 11

For $z$ , we have $z =3x =3 \times19$

STEP 12

Calculate the value of $z$ .
$z = \times19 =57$ The first number is19, the second number is10, and the third number is57.

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QuestionFind three numbers where their sum is 86, the second is 9 less than the first, and the third is 3 times the first.

Studdy Solution

STEP 1

Assumptions1. The sum of three numbers is86. The second number is9 less than the first number3. The third number is3 times the first number

STEP 2

Let's denote the first number as $x$ , the second number as $y$ , and the third number as $z$ . We can write the given conditions as equations1. $x + y + z =86$
2. $y = x -9$ . $z =x$

STEP 3

Now, we can substitute the expressions for $y$ and $z$ from the second and third equations into the first equation.
$x + (x -9) +3x =86$

STEP 4

implify the equation by combining like terms.
$x -9 =86$

STEP 5

Add9 to both sides of the equation to isolate the term with $x$ .
$5x =86 +9$

STEP 6

implify the right side of the equation.
$5x =95$

STEP 7

Divide both sides of the equation by5 to solve for $x$ .
$x = \frac{95}{5}$

STEP 8

Calculate the value of $x$ .
$x = \frac{95}{5} =19$

STEP 9

Now that we have the value of $x$ , we can find the values of $y$ and $z$ by substituting $x =19$ into the equations $y = x -9$ and $z =3x$ .
For $y$ , we have $y = x -9 =19 -9$

STEP 10

Calculate the value of $y$ .
$y =19 -9 =10$

STEP 11

For $z$ , we have $z =3x =3 \times19$

STEP 12

Calculate the value of $z$ .
$z = \times19 =57$ The first number is19, the second number is10, and the third number is57.

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QuestionFind three numbers where their sum is 86, the second is 9 less than the first, and the third is 3 times the first.

Studdy Solution

STEP 1

Assumptions1. The sum of three numbers is86. The second number is9 less than the first number3. The third number is3 times the first number

STEP 2

Let's denote the first number as xxx, the second number as yyy, and the third number as zzz. We can write the given conditions as equations1. x+y+z=86x + y + z =86x+y+z=862. y=x−9y = x -9y=x−9 . z=xz =xz=x

STEP 3

Now, we can substitute the expressions for yyy and zzz from the second and third equations into the first equation.x+(x−9)+3x=86x + (x -9) +3x =86x+(x−9)+3x=86

STEP 4

implify the equation by combining like terms.x−9=86x -9 =86x−9=86

STEP 5

Add9 to both sides of the equation to isolate the term with xxx.5x=86+95x =86 +95x=86+9

STEP 6

implify the right side of the equation.5x=955x =955x=95

STEP 7

Divide both sides of the equation by5 to solve for xxx.x=955x = \frac{95}{5}x=595​

STEP 8

Calculate the value of xxx.x=955=19x = \frac{95}{5} =19x=595​=19

STEP 9

Now that we have the value of xxx, we can find the values of yyy and zzz by substituting x=19x =19x=19 into the equations y=x−9y = x -9y=x−9 and z=3xz =3xz=3x.For yyy, we havey=x−9=19−9y = x -9 =19 -9y=x−9=19−9

STEP 10

Calculate the value of yyy.y=19−9=10y =19 -9 =10y=19−9=10

STEP 11

For zzz, we havez=3x=3×19z =3x =3 \times19z=3x=3×19

STEP 12

Calculate the value of zzz.z=×19=57z = \times19 =57z=×19=57The first number is19, the second number is10, and the third number is57.

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Let's denote the first number as $x$ , the second number as $y$ , and the third number as $z$ . We can write the given conditions as equations1. $x + y + z =86$
2. $y = x -9$ . $z =x$

Now, we can substitute the expressions for $y$ and $z$ from the second and third equations into the first equation.
$x + (x -9) +3x =86$

implify the equation by combining like terms.
$x -9 =86$

Add9 to both sides of the equation to isolate the term with $x$ .
$5x =86 +9$

implify the right side of the equation.
$5x =95$

Divide both sides of the equation by5 to solve for $x$ .
$x = \frac{95}{5}$

Calculate the value of $x$ .
$x = \frac{95}{5} =19$

Now that we have the value of $x$ , we can find the values of $y$ and $z$ by substituting $x =19$ into the equations $y = x -9$ and $z =3x$ .
For $y$ , we have $y = x -9 =19 -9$

Calculate the value of $y$ .
$y =19 -9 =10$

For $z$ , we have $z =3x =3 \times19$

Calculate the value of $z$ .
$z = \times19 =57$ The first number is19, the second number is10, and the third number is57.