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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

In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the percent decrease.
Jenise Reply
how do i set this up
Jenise
25%
Melissa
25 percent
Muzamil
950,000 - 712,500 = 237,500. 237,500 / 950,000 = .25 = 25%
Melissa
I've tried several times it won't let me post the breakdown of how you get 25%.
Melissa
Subtract one from the other to get the difference. Then take that difference and divided by 950000 and you will get .25 aka 25%
Melissa
Finally 👍
Melissa
one way is to set as ratio: 100%/950000 = x% / 712500, which yields that 712500 is 75% of the initial 950000. therefore, the decrease is 25%.
bruce
twenty five percent...
Jeorge
thanks melissa
Jeorge
950000-713500 *100 and then divide by 950000 = 25
Muzamil
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
jamie Reply
6t+3
Melissa
6t +3
Bollywood
Tricia got a 6% raise on her weekly salary. The raise was $30 per week. What was her original salary?
Iris Reply
let us suppose her original salary is 'm'. so, according to the given condition, m*(6/100)=30 m= (30*100)/6 m= 500 hence, her original salary is $500.
Simply
28.50
Toi
thanks
Jeorge
How many pounds of nuts selling for $6 per pound and raisins selling for $3 per pound should Kurt combine to obtain 120 pounds of trail mix that cost him $5 per pound?
Valeria Reply
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost $8 per square foot and decorator tiles that code $20 per square foot. How many square feet of each tile should she use so that the overal cost of he backsplash will be $10 per square foot?
Nia Reply
I need help with maths can someone help me plz.. is there a wats app group?
Cindy Reply
WY need
Fernando
How did you get $750?
Laura Reply
if y= 2x+sinx what is dy÷dx
formon25 Reply
does it teach you how to do algebra if you don't know how
Kate Reply
Liam borrowed a total of $35,000 to pay for college. He pays his parents 3% interest on the $8,000 he borrowed from them and pays the bank 6.8% on the rest. What average interest rate does he pay on the total $35,000? (Round your answer to the nearest tenth of a percent.)
Lara Reply
exact definition of length by bilbao
francemichael Reply
the definition of length
francemichael Reply
literal meaning of length
francemichael
exact meaning of length
francemichael
exact meaning of length
francemichael
how many typos can we find...?
Chris Reply
5
Joseph
In the LCM Prime Factors exercises, the LCM of 28 and 40 is 280. Not 420!
Chris Reply
4x+7y=29,x+3y=11 substitute method of linear equation
Srinu Reply
substitute method of linear equation
Srinu
Solve one equation for one variable. Using the 2nd equation, x=11-3y. Substitute that for x in first equation. this will find y. then use the value for y to find the value for x.
bruce
I want to learn
Elizebeth
help
Elizebeth
I want to learn. Please teach me?
Wayne
1) Use any equation, and solve for any of the variables. Since the coefficient of x (the number in front of the x) in the second equation is 1 (it actually isn't shown, but 1 * x = x), use that equation. Subtract 3y from both sides (this isolates the x on the left side of the equal sign).
bruce
2) This results in x=11-3y. x is note in terms of y. Use that as the value of x and substitute for all x in the first equation. The first equation becomes 4(11-3y)+7y =29. Note that the only variable left in the first equation is the y. If you have multiple variable, then something is wrong.
bruce
3) Distribute (multiply) the 4 across 11-3y to get 44-12y. Add this to the 7y. So, the equation is now 44-5y=29.
bruce
4) Solve 44-5y=29 for y. Isolate the y by subtracting 44 from birth sides, resulting in -5y=-15. Now, divide birth sides by -5 (since you have -5y). This results in y=3. You now have the value of one variable.
bruce
5) The last step is to take the value of y from Step 4) and substitute into the 2nd equation. Therefore: x+3y=11 becomes x+3(3)=11. Then multiplying, x+9=11. Finally, solve for x by subtracting 9 from both sides. Therefore, x=2.
bruce
6) The ordered pair of (2, 3) is the proposed solution. To check, substitute those values into either equation. If the result is true, then the solution is correct. 4(2)+7(3)=8+21=29. TRUE! Finished.
bruce

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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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