QuestionFind three numbers: one is 9 times the first, another is 100 more than the first, and their sum is 364. What are they?

Studdy Solution

STEP 1

Assumptions1. Let's denote the first number as $x$ . . The second number is9 times the first number, so we can denote it as $9x$ .
3. The third number is100 more than the first number, so we can denote it as $x +100$ .
4. The sum of the three numbers is364.

STEP 2

Now, we can write an equation based on the given information. The sum of the three numbers is equal to364.
$x +9x + (x +100) =364$

STEP 3

implify the equation by combining like terms.
$11x +100 =364$

STEP 4

Subtract100 from both sides of the equation to isolate the term with $x$ .
$11x =364 -100$

STEP 5

Calculate the right side of the equation.
$11x =264$

STEP 6

Divide both sides of the equation by11 to solve for $x$ .
$x = \frac{264}{11}$

STEP 7

Calculate the value of $x$ .
$x =24$

STEP 8

Now that we have the value for $x$ , we can find the values of the other two numbers. The second number is times the first number.
$x = \times24$

STEP 9

Calculate the value of the second number.
$9x =216$

STEP 10

The third number is100 more than the first number.
$(x +100) =24 +100$

STEP 11

Calculate the value of the third number.
$(x +100) =124$ The three numbers are24,216, and124.

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QuestionFind three numbers: one is 9 times the first, another is 100 more than the first, and their sum is 364. What are they?

Studdy Solution

STEP 1

Assumptions1. Let's denote the first number as $x$ . . The second number is9 times the first number, so we can denote it as $9x$ .
3. The third number is100 more than the first number, so we can denote it as $x +100$ .
4. The sum of the three numbers is364.

STEP 2

Now, we can write an equation based on the given information. The sum of the three numbers is equal to364.
$x +9x + (x +100) =364$

STEP 3

implify the equation by combining like terms.
$11x +100 =364$

STEP 4

Subtract100 from both sides of the equation to isolate the term with $x$ .
$11x =364 -100$

STEP 5

Calculate the right side of the equation.
$11x =264$

STEP 6

Divide both sides of the equation by11 to solve for $x$ .
$x = \frac{264}{11}$

STEP 7

Calculate the value of $x$ .
$x =24$

STEP 8

Now that we have the value for $x$ , we can find the values of the other two numbers. The second number is times the first number.
$x = \times24$

STEP 9

Calculate the value of the second number.
$9x =216$

STEP 10

The third number is100 more than the first number.
$(x +100) =24 +100$

STEP 11

Calculate the value of the third number.
$(x +100) =124$ The three numbers are24,216, and124.

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QuestionFind three numbers: one is 9 times the first, another is 100 more than the first, and their sum is 364. What are they?

Studdy Solution

STEP 1

Assumptions1. Let's denote the first number as xxx. . The second number is9 times the first number, so we can denote it as 9x9x9x.3. The third number is100 more than the first number, so we can denote it as x+100x +100x+100.4. The sum of the three numbers is364.

STEP 2

Now, we can write an equation based on the given information. The sum of the three numbers is equal to364.x+9x+(x+100)=364x +9x + (x +100) =364x+9x+(x+100)=364

STEP 3

implify the equation by combining like terms.11x+100=36411x +100 =36411x+100=364

STEP 4

Subtract100 from both sides of the equation to isolate the term with xxx.11x=364−10011x =364 -10011x=364−100

STEP 5

Calculate the right side of the equation.11x=26411x =26411x=264

STEP 6

Divide both sides of the equation by11 to solve for xxx.x=26411x = \frac{264}{11}x=11264​

STEP 7

Calculate the value of xxx.x=24x =24x=24

STEP 8

Now that we have the value for xxx, we can find the values of the other two numbers. The second number is times the first number.x=×24x = \times24x=×24

STEP 9

Calculate the value of the second number.9x=2169x =2169x=216

STEP 10

The third number is100 more than the first number.(x+100)=24+100(x +100) =24 +100(x+100)=24+100

STEP 11

Calculate the value of the third number.(x+100)=124(x +100) =124(x+100)=124The three numbers are24,216, and124.

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Assumptions1. Let's denote the first number as $x$ . . The second number is9 times the first number, so we can denote it as $9x$ .
3. The third number is100 more than the first number, so we can denote it as $x +100$ .
4. The sum of the three numbers is364.

Now, we can write an equation based on the given information. The sum of the three numbers is equal to364.
$x +9x + (x +100) =364$

implify the equation by combining like terms.
$11x +100 =364$

Subtract100 from both sides of the equation to isolate the term with $x$ .
$11x =364 -100$

Calculate the right side of the equation.
$11x =264$

Divide both sides of the equation by11 to solve for $x$ .
$x = \frac{264}{11}$

Calculate the value of $x$ .
$x =24$

Now that we have the value for $x$ , we can find the values of the other two numbers. The second number is times the first number.
$x = \times24$

Calculate the value of the second number.
$9x =216$

The third number is100 more than the first number.
$(x +100) =24 +100$

Calculate the value of the third number.
$(x +100) =124$ The three numbers are24,216, and124.