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

when I = $ 5,400 , r = 12 % , t = 5 years in general

$9,000 P = I r 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 .

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

when x = 4 in general

Solution

when x = 4 in general
. .
Substitute. .
Subtract to isolate the
y -term.
. Subtract to isolate the
y -term.
.
Divide. . Divide. .
Simplify. . Simplify. .
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Solve the formula 3 x + 4 y = 10 for y :

when x = 14 3 in general

y = 1 y = 10 3 x 4

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

when x = 4 in general

y = −1 y = 18 5 x 2

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In Examples 1.60 through 1.64 we used the numbers in part as a guide to solving in general in part . Now we will 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. .
Both b and c are added to a , so we subtract them from both sides of the equation. .
Simplify. .
.
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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 formula 6 x + 5 y = 13 for y.

Solution

.
Subtract 6 x from both sides to isolate the term with y . .
Simplify. .
Divide by 5 to make the coefficient 1. .
Simplify. .

The fraction is simplified. We cannot divide 13 6 x by 5.

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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

  • To Solve an Application (with a formula)
    1. Read the problem. Make sure all the words and ideas are understood.
    2. Identify what we are looking for.
    3. Name what we are looking for. Choose a variable to represent that quantity.
    4. Translate into an equation. Write the appropriate formula for the situation. Substitute in the given information.
    5. Solve the equation using good algebra techniques.
    6. Check the answer in the problem and make sure it makes sense.
    7. Answer the question with a complete sentence.
  • Distance, Rate and Time
    For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: d = r t where d = distance, r = rate, t = time.
  • To solve a formula for a specific variable means to get that variable by itself with a coefficient of 1 on one side of the equation and all other variables and constants on the other side.

Practice makes perfect

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

Steve drove for 8 1 2 hours at 72 miles per hour. How much distance did he travel?

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Socorro drove for 4 5 6 hours at 60 miles per hour. How much distance did she travel?

290 miles

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Yuki walked for 1 3 4 hours at 4 miles per hour. How far did she walk?

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Francie rode her bike for 2 1 2 hours at 12 miles per hour. How far did she ride?

30 miles

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Connor wants to drive from Tucson to the Grand Canyon, a distance of 338 miles. If he drives at a steady rate of 52 miles per hour, how many hours will the trip take?

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Megan is taking the bus from New York City to Montreal. The distance is 380 miles and the bus travels at a steady rate of 76 miles per hour. How long will the bus ride be?

5 hours

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Questions & Answers

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sammie Reply
physiological Psychology
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Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
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Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
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nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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