# 2.6 Solve a formula for a specific variable  (Page 3/4)

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Use the formula $I=Prt$ to find the principal, $P$ :

when $I=\text{}5,400,r=12%,t=5\phantom{\rule{0.2em}{0ex}}\text{years}\phantom{\rule{0.2em}{0ex}}$ in general

$9,000 $P=\frac{I}{rt}$ 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 $3x+2y=18$ 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. Solve the formula $3x+4y=10$ for y : when $x=\frac{14}{3}$ in general $y=1$ $y=\frac{10-3x}{4}$ Solve the formula $5x+2y=18$ for y: when $x=4$ in general $y=-1$ $y=\frac{18-5x}{2}$ 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.  Solve the formula $P=a+b+c$ for b . $b=P-a-c$ Solve the formula $P=a+b+c$ for c . $c=P-a-b$ Solve the formula $6x+5y=13$ for y. ## Solution Subtract $6x$ 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 $13-6x$ by 5. Solve the formula $4x+7y=9$ for y. $y=\frac{9-4x}{7}$ Solve the formula $5x+8y=1$ for y. $y=\frac{1-5x}{8}$ ## 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: $d=rt$ 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. Steve drove for $8\frac{1}{2}$ hours at 72 miles per hour. How much distance did he travel? Socorro drove for $4\frac{5}{6}$ hours at 60 miles per hour. How much distance did she travel? 290 miles Yuki walked for $1\frac{3}{4}$ hours at 4 miles per hour. How far did she walk? Francie rode her bike for $2\frac{1}{2}$ hours at 12 miles per hour. How far did she ride? 30 miles 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? 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 #### Questions & Answers rectangular field solutions Navin Reply What is this? Donna the proudact of 3x^3-5×^2+3 and 2x^2+5x-4 in z7[x]/ is anas Reply ? Choli a rock is thrown directly upward with an initial velocity of 96feet per second from a cliff 190 feet above a beach. The hight of tha rock above the beach after t second is given by the equation h=_16t^2+96t+190 Usman Stella bought a dinette set on sale for$725. The original price was $1,299. To the nearest tenth of a percent, what was the rate of discount? Manhwa Reply 44.19% Scott 40.22% Terence 44.2% Orlando I don't know Donna if you want the discounted price subtract$725 from $1299. then divide the answer by$1299. you get 0.4419... but as percent you get 44.19... but to the nearest tenth... round .19 to .2 and you get 44.2%
Orlando
you could also just divide $725/$1299 and then subtract it from 1. then you get the same answer.
Orlando
p mulripied-5 and add 30 to it
Tausif
Tausif
Can you explain further
p mulripied-5 and add to 30
Tausif
How do you find divisible numbers without a calculator?
TAKE OFF THE LAST DIGIT AND MULTIPLY IT 9. SUBTRACT IT THE DIGITS YOU HAVE LEFT. IF THE ANSWER DIVIDES BY 13(OR IS ZERO), THEN YOUR ORIGINAL NUMBER WILL ALSO DIVIDE BY 13!IS DIVISIBLE BY 13
BAINAMA
When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was$1,585. What is the amount of each loan?
Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 7 2/3 hours, what was the speed of the bus?
66miles/hour
snigdha
How did you work it out?
Esther
s=mi/hr 2/3~0.67 s=506mi/7.67hr = ~66 mi/hr
Orlando
hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused.
what do you need help in?
Felix
Heather
look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number...
Felix
for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer...
Felix
—12
Thanks Felix.l also get confused with signs.
Esther
Thank you for this
Shatey
ty
Graham
think about it like you lost $19 (-19), then found$7(+7). Totally you lost just $12 (-12) Annushka I used to struggle a lot with negative numbers and math in general what I typically do is look at it in terms of money I have -$5 in my account I then take out 5 more dollars how much do I have in my account well-\$10 ... I also for a long time would draw it out on a number line to visualize it
Meg
practicing with smaller numbers to understand then working with larger numbers helps too and the song/rhyme same sign add and keep opposite signs subtract keep the sign of the bigger # then you'll be exact
Meg
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
168.50=R
Heather
john is 5years older than wanjiru.the sum of their years is27years.what is the age of each
46
mustee
j 17 w 11
Joseph
john is 16. wanjiru is 11.
Felix
27-5=22 22÷2=11 11+5=16
Joyce
I don't see where the answers are.
Ed
Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart?
3
Christopher
18t+14t=96 32t=96 32/96 3
Christopher
show that a^n-b^2n is divisible by a-b
What does 3 times your weight right now
Use algebra to combine 39×5 and the half sum of travel of 59+30
Cherokee
What is the segment of 13? Explain
Cherokee
my weight is 49. So 3 times is 147
Cherokee
kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps
tyler
How to convert grams to pounds?
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