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Use the formula A = 1 2 b h to solve for h:

  1. when A = 170 and b = 17
  2. in general

h = 20 h = 2 A b

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Use the formula A = 1 2 b h to solve for b :

  1. when A = 62 and h = 31
  2. in general

  1. b = 4
  2. b = 2 A h
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In Solve Simple Interest Applications , we used the formula I = P r t to calculate simple interest, where I is interest, P is principal, r is rate as a decimal, and t is time in years.

Solve the formula I = P r t to find the principal, P :

  1. when I = $5,600 , r = 4% , t = 7 years
  2. in general

Solution

I = $5600, r = 4%, t = 7 years in general
Write the forumla. . .
Substitute any given values. . .
Multiply r t . . .
Divide to isolate P . . .
Simplify. . .
State the answer. The principal is $20,000. .
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Use the formula I = P r t .

Find t : when I = $2,160 , r = 6% , P = $12,000; in general

  1. t = 3 years
  2. t = I P r

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Use the formula I = P r t .

Find r : when I = $5,400 , P = $9,000 , t = 5 years in general

  1. r = 0.12 = 12%
  2. r = I P t

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Later in this class, and in future algebra classes, you’ll encounter equations that relate two variables, usually x and y . You might be given an equation that is solved for y and need to solve it for x , or vice versa. In the following example, we’re given an equation with both x and y on the same side and we’ll solve it for y . To do this, we will follow the same steps that we used to solve a formula for a specific variable.

Solve the formula 3 x + 2 y = 18 for y :

  1. when x = 4
  2. in general

Solution

when x = 4 in general
Write the equation. . .
Substitute any given values. . .
Simplify if possible. . .
Subtract to isolate the y -term. . .
Simplify. . .
Divide. . .
Simplify. . .
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Solve the formula 3 x + 4 y = 10 for y :

  1. when x = 2
  2. in general

  1. y = 1
  2. y = 10 3 x 4

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Solve the formula 5 x + 2 y = 18 for y :

  1. when x = 4
  2. in general

  1. y = −1
  2. y = 18 5 x 2

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In the previous examples, we used the numbers in part (a) as a guide to solving in general in part (b). Do you think you’re ready to solve a formula in general without using numbers as a guide?

Solve the formula P = a + b + c for a .

Solution

We will isolate a on one side of the equation.

We will isolate a on one side of the equation.
Write the equation. P = a + b + c
Subtract b and c from both sides to isolate a . .
Simplify. P b c = a

So, a = P b c

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Solve the formula P = a + b + c for b .

b = P a c

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Solve the formula P = a + b + c for c .

c = P a b

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Solve the equation 3 x + y = 10 for y .

Solution

We will isolate y on one side of the equation.

We will isolate y on one side of the equation.
Write the equation. 3 x + y = 10
Subtract 3 x from both sides to isolate y . .
Simplify. y = 10 3 x

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Solve the formula 7 x + y = 11 for y .

y = 11 − 7 x

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Solve the formula 11 x + y = 8 for y .

y = 8 − 11 x

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Solve the equation 6 x + 5 y = 13 for y .

Solution

We will isolate y on one side of the equation.

We will isolate y on one side of the equation.
Write the equation. .
Subtract to isolate the term with y . .
Simplify. .
Divide 5 to make the coefficient 1. .
Simplify. .

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Solve the formula 4 x + 7 y = 9 for y .

y = 9 4 x 7

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Solve the formula 5 x + 8 y = 1 for y .

y = 1 5 x 8

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Key concepts

  • Distance, Rate, and Time
    • d = r t

Practice makes perfect

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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