QuestionTower A is 898 feet taller than Tower B, and together they are 1,712 feet. Find the height of Tower B.

Studdy Solution

STEP 1

Assumptions1. The height of Tower A is898 feet more than Tower B. . The combined height of the two towers is1,712 feet.

STEP 2

Let's denote the height of Tower B as $h_B$ and the height of Tower A as $h_A$ . According to the problem, we have two equations1. $h_A = h_B +898$ (Tower A is898 feet taller than Tower B)
2. $h_A + h_B =1712$ (The combined height of the two towers is1712 feet)

STEP 3

We can substitute the first equation into the second equation to solve for $h_B$ .
$h_B +898 + h_B =1712$

STEP 4

Combine like terms.
$2h_B +898 =1712$

STEP 5

Subtract898 from both sides of the equation to isolate $2h_B$ .
$2h_B =1712 -898$

STEP 6

Calculate the right side of the equation.
$2h_B =814$

STEP 7

Divide both sides of the equation by2 to solve for $h_B$ .
$h_B =814 /2$

STEP 8

Calculate the value of $h_B$ .
$h_B =407$ So, Tower B is407 feet tall.

STEP 9

Now, we can substitute $h_B$ into the first equation to solve for $h_A$ .
$h_A =407 +898$

STEP 10

Calculate the value of $h_A$ .
$h_A =1305$ So, Tower A is1305 feet tall.
The heights of the towers are407 feet (Tower B) and1305 feet (Tower A).

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QuestionTower A is 898 feet taller than Tower B, and together they are 1,712 feet. Find the height of Tower B.

Studdy Solution

STEP 1

Assumptions1. The height of Tower A is898 feet more than Tower B. . The combined height of the two towers is1,712 feet.

STEP 2

Let's denote the height of Tower B as $h_B$ and the height of Tower A as $h_A$ . According to the problem, we have two equations1. $h_A = h_B +898$ (Tower A is898 feet taller than Tower B)
2. $h_A + h_B =1712$ (The combined height of the two towers is1712 feet)

STEP 3

We can substitute the first equation into the second equation to solve for $h_B$ .
$h_B +898 + h_B =1712$

STEP 4

Combine like terms.
$2h_B +898 =1712$

STEP 5

Subtract898 from both sides of the equation to isolate $2h_B$ .
$2h_B =1712 -898$

STEP 6

Calculate the right side of the equation.
$2h_B =814$

STEP 7

Divide both sides of the equation by2 to solve for $h_B$ .
$h_B =814 /2$

STEP 8

Calculate the value of $h_B$ .
$h_B =407$ So, Tower B is407 feet tall.

STEP 9

Now, we can substitute $h_B$ into the first equation to solve for $h_A$ .
$h_A =407 +898$

STEP 10

Calculate the value of $h_A$ .
$h_A =1305$ So, Tower A is1305 feet tall.
The heights of the towers are407 feet (Tower B) and1305 feet (Tower A).

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QuestionTower A is 898 feet taller than Tower B, and together they are 1,712 feet. Find the height of Tower B.

Studdy Solution

STEP 1

Assumptions1. The height of Tower A is898 feet more than Tower B. . The combined height of the two towers is1,712 feet.

STEP 2

STEP 3

We can substitute the first equation into the second equation to solve for hBh_BhB​.hB+898+hB=1712h_B +898 + h_B =1712hB​+898+hB​=1712

STEP 4

Combine like terms.2hB+898=17122h_B +898 =17122hB​+898=1712

STEP 5

Subtract898 from both sides of the equation to isolate 2hB2h_B2hB​.2hB=1712−8982h_B =1712 -8982hB​=1712−898

STEP 6

Calculate the right side of the equation.2hB=8142h_B =8142hB​=814

STEP 7

Divide both sides of the equation by2 to solve for hBh_BhB​.hB=814/2h_B =814 /2hB​=814/2

STEP 8

Calculate the value of hBh_BhB​.hB=407h_B =407hB​=407So, Tower B is407 feet tall.

STEP 9

Now, we can substitute hBh_BhB​ into the first equation to solve for hAh_AhA​.hA=407+898h_A =407 +898hA​=407+898

STEP 10

Calculate the value of hAh_AhA​.hA=1305h_A =1305hA​=1305So, Tower A is1305 feet tall.The heights of the towers are407 feet (Tower B) and1305 feet (Tower A).

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We can substitute the first equation into the second equation to solve for $h_B$ .
$h_B +898 + h_B =1712$

Combine like terms.
$2h_B +898 =1712$

Subtract898 from both sides of the equation to isolate $2h_B$ .
$2h_B =1712 -898$

Calculate the right side of the equation.
$2h_B =814$

Divide both sides of the equation by2 to solve for $h_B$ .
$h_B =814 /2$

Calculate the value of $h_B$ .
$h_B =407$ So, Tower B is407 feet tall.

Now, we can substitute $h_B$ into the first equation to solve for $h_A$ .
$h_A =407 +898$

Calculate the value of $h_A$ .
$h_A =1305$ So, Tower A is1305 feet tall.
The heights of the towers are407 feet (Tower B) and1305 feet (Tower A).