



Use the formula
$I=Prt$ to find the principal,
$P$ :
ⓐ when
$I=\text{\$}\mathrm{5,400},r=12\%,t=5\phantom{\rule{0.2em}{0ex}}\text{years}\phantom{\rule{0.2em}{0ex}}$
ⓑ in general
ⓐ $9,000
ⓑ
$P=\frac{I}{rt}$
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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 .
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.
Key concepts

To Solve an Application (with a formula)

Read the problem. Make sure all the words and ideas are understood.

Identify what we are looking for.

Name what we are looking for. Choose a variable to represent that quantity.

Translate into an equation. Write the appropriate formula for the situation. Substitute in the given information.

Solve the equation using good algebra techniques.

Check the answer in the problem and make sure it makes sense.

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:
$d=rt$ 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.
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?
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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.
how do i set this up
Jenise
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
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
950000713500 *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.
Tricia got a 6% raise on her weekly salary. The raise was $30 per week. What was her original salary?
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
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?
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?
I need help with maths can someone help me plz..
is there a wats app group?
if y= 2x+sinx
what is dy÷dx
does it teach you how to do algebra if you don't know how
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.)
exact definition of length by bilbao
literal meaning of length
francemichael
exact meaning of length
francemichael
exact meaning of length
francemichael
how many typos can we find...?
In the LCM Prime Factors exercises, the LCM of 28 and 40 is 280. Not 420!
4x+7y=29,x+3y=11 substitute method of linear equation
substitute method of linear equation
Srinu
Solve one equation for one variable. Using the 2nd equation, x=113y. 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
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=113y. 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(113y)+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 113y to get 4412y. Add this to the 7y. So, the equation is now 445y=29.
bruce
4) Solve 445y=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
Source:
OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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