



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
Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs $6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs $5.71 per gallon?
(a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r)
4x7y=8
2x7y=1
what is the answer?
x=7/2 & y=6/7
use Elimination
Debra
4x7y=8
X=7/4y+2 and 2x7y=1 x=7/2y+1/2
Peggie
Ok cool answer peggie
Frank
copy and complete the table. x. 5. 8. 12. then 9x5. to the 2nd power+4. then 2xto the second power +3x
C+4=8
4 4
C =4
thinking
During two years in college, a student earned $9,500. The second year, she earned $500 more than twice the amount she earned the first year.
9500500=9000
9000÷2×=4500
X=4500
Debra
X + Y = 9500....... &
Y = 500 + 2X
so.... X + 500 + 2X = 9500,
them X = 3000 & Y = 6500
Pbp
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles.
Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than $500. The number of cards is at least 4 more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is $3 and for a package the cost is $7.
The sum of two numbers is 155. The difference is 23. Find the numbers
The sum of two numbers is 155. Their difference is 23. Find the numbers
Michelle
The difference between 89 and 66 is 23
Ciid
Joy is preparing 20 liters of a 25% saline solution. She only has 40% and 10% solution in her lab. How many liters of the 40% and how many liters of the 10% should she mix to make the 25% solution?
I need a math tutor BAD
Stacie
Sue and Deb work together writing a book that takes them 90 days. If Sue worked alone, it would take her 120 days. How long would it take Deb to write the book alone?
Tell Deb to write the book alone and report back on how long it took her. Deb could get bored and stop, she could get sick next week and prolong the time, she could die next month. This question is impossible to answer.
vV
is there a thumbs up mathematical symbol in algebra? 👍²= vV
90days x 120days =10800
120days  90days = 30
10800days/30days= 360days?
(ad) derall=1440 mins
(90x ad )+(120 x ad )/(120 x ad ))((90d x ad)= you go glen coco!
I'll see my self out
Nick
Larry and Tom were standing next to each other in the backyard when Tom challenged Larry to guess how tall he was. Larry knew his own height is 6.5 feet and when they measured their shadows, Larry’s shadow was 8 feet and Tom’s was 7.75 feet long. What is Tom’s height?
Wayne is hanging a string of lights 57 feet long around the three sides of his patio, which is adjacent to his house. the length of his patio, the side along the house, is 5 feet longer than twice it's width. Find the length and width of the patio.
complexed. could you please help me figure out?
Ciid
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
SOH = Sine is Opposite over Hypotenuse. CAH= Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent.
tyler
H=57 and O=285 figure out what the adjacent?
tyler
draw a diagram first
John
Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
what is the quantity and price of the televisions for both options?
karl
Amara has to sell 120 televisions to make 29,000 of the salary of company B.
120 * TV
100= commission
12,000+
17,000 = of company a salary
29,000
17000+
Ciid
Amara has to sell 120 televisions to make 29,000 of the salary of company B.
120 * TV
100= commission
12,000+
17,000 = of company a salary
29,000
Ciid
I'm mathematics teacher from highly recognized university.
here a question professor How many soldiers are there in a group of 27 sailors and soldiers if there
are four fifths as many sailors as soldiers? can you write out the college you went to with the name of the school you teach at and let me know the answer I've got it to be honest with you
tyler
Source:
OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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