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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

a=# of 10's. b=# of 20's; a+b=54; 10a + 20b=$910; a=54 -b; 10(54-b) + 20b=$910; 540-10b+20b=$910; 540+10b=$910; 10b=910-540; 10b=370; b=37; so there are 37 20's and since a+b=54, a+37=54; a=54-37=17; a=17, so 17 10's. So lets check. $740+$170=$910.
David Reply
. A cashier has 54 bills, all of which are $10 or $20 bills. The total value of the money is $910. How many of each type of bill does the cashier have?
jojo Reply
whats the coefficient of 17x
Dwayne Reply
the solution says it 14 but how i thought it would be 17 im i right or wrong is the exercise wrong
Dwayne
17
Melissa
wow the exercise told me 17x solution is 14x lmao
Dwayne
thank you
Dwayne
A private jet can fly 1,210 miles against a 25 mph headwind in the same amount of time it can fly 1,694 miles with a 25 mph tailwind. Find the speed of the jet
Mikaela Reply
Washing his dad’s car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
Sam Reply
Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, they meet on the path. Ethan’s speed is 6 miles per hour faster than Leo’s speed. Find the speed of the two bikers.
Mckenzie Reply
Nathan walked on an asphalt pathway for 12 miles. He walked the 12 miles back to his car on a gravel road through the forest. On the asphalt he walked 2 miles per hour faster than on the gravel. The walk on the gravel took one hour longer than the walk on the asphalt. How fast did he walk on the gravel?
Mckenzie
Nancy took a 3 hour drive. She went 50 miles before she got caught in a storm. Then she drove 68 miles at 9 mph less than she had driven when the weather was good. What was her speed driving in the storm?
Reiley Reply
Mr Hernaez runs his car at a regular speed of 50 kph and Mr Ranola at 36 kph. They started at the same place at 5:30 am and took opposite directions. At what time were they 129 km apart?
hamzzi Reply
90 minutes
muhammad
Melody wants to sell bags of mixed candy at her lemonade stand. She will mix chocolate pieces that cost $4.89 per bag with peanut butter pieces that cost $3.79 per bag to get a total of twenty-five bags of mixed candy. Melody wants the bags of mixed candy to cost her $4.23 a bag to make. How many bags of chocolate pieces and how many bags of peanut butter pieces should she use?
Jake Reply
enrique borrowed $23,500 to buy a car he pays his uncle 2% interest on the $4,500 he borrowed from him and he pays the bank 11.5% interest on the rest. what average interest rate does he pay on the total $23,500
Nakiya Reply
13.5
Pervaiz
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 cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot?
Bridget Reply
The equation P=28+2.54w models the relation between the amount of Randy’s monthly water bill payment, P, in dollars, and the number of units of water, w, used. Find the payment for a month when Randy used 15 units of water.
Bridget
help me understand graphs
Marlene Reply
what kind of graphs?
bruce
function f(x) to find each value
Marlene
I am in algebra 1. Can anyone give me any ideas to help me learn this stuff. Teacher and tutor not helping much.
Marlene
Given f(x)=2x+2, find f(2) so you replace the x with the 2, f(2)=2(2)+2, which is f(2)=6
Melissa
if they say find f(5) then the answer would be f(5)=12
Melissa
I need you to help me Melissa. Wish I can show you my homework
Marlene
How is f(1) =0 I am really confused
Marlene
what's the formula given? f(x)=?
Melissa
It shows a graph that I wish I could send photo of to you on here
Marlene
Which problem specifically?
Melissa
which problem?
Melissa
I don't know any to be honest. But whatever you can help me with for I can practice will help
Marlene
I got it. sorry, was out and about. I'll look at it now.
Melissa
Thank you. I appreciate it because my teacher assumes I know this. My teacher before him never went over this and several other things.
Marlene
I just responded.
Melissa
Thank you
Marlene
-65r to the 4th power-50r cubed-15r squared+8r+23 ÷ 5r
WENDY Reply
State the question clearly please
Rich
write in this form a/b answer should be in the simplest form 5%
August Reply
convert to decimal 9/11
August
0.81818
Rich
5/100 = .05 but Rich is right that 9/11 = .81818
Melissa
Equation in the form of a pending point y+2=1/6(×-4)
Jose Reply
write in simplest form 3 4/2
August

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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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