# 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 Aziza is solving this equation-2(1+x)=4x+10 Sechabe Reply No. 3^32 -1 has exactly two divisors greater than 75 and less than 85 what is their product? KAJAL Reply x^2+7x-19=0 has Two solutions A and B give your answer to 3 decimal places Adedamola Reply please the answer to the example exercise Patricia Reply 3. When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes onthe elliptical trainer and 30 minutes circuit training she burned 473 calories. How manycalories does she burn for each minute on the elliptical trainer? How many calories doesshe burn for each minute of circuit training? Edwin Reply .473 Angelita ? Angelita John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18. DaYoungan Reply p-2/3=5/6 how do I solve it with explanation pls Adedamola Reply P=3/2 Vanarith 1/2p2-2/3p=5p/6 James don't understand answer Cindy 4.5 Ruth is y=7/5 a solution of 5y+3=10y-4 Adedamola Reply yes James don't understand answer Cindy Lucinda has a pocketful of dimes and quarters with a value of$6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have?
Find an equation for the line that passes through the point P ( 0 , − 4 ) and has a slope 8/9 .
is that a negative 4 or positive 4?
Felix
y = mx + b
Felix
if negative -4, then -4=8/9(0) + b
Felix
-4=b
Felix
if positive 4, then 4=b
Felix
then plug in y=8/9x - 4 or y=8/9x+4
Felix
Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. macadamia nuts cost $9 per pound and almonds cost$5.25 per pound. how many pounds of macadamia nuts and how many pounds of almonds should macario use for the mixture to cost $6.50 per pound to make? Cherry Reply Nga and Lauren bought a chest at a flea market for$50. They re-finished it and then added a 350 % mark - up
\$1750
Cindy
the sum of two Numbers is 19 and their difference is 15
2, 17
Jose
interesting
saw
4,2
Cindy
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 13 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
hola saben como aser un valor de la expresión
NAILEA
integer greater than 2 and less than 12
2 < x < 12
Felix
I'm guessing you are doing inequalities...
Felix
Actually, translating words into algebraic expressions / equations...
Felix
hi
Darianna
hello
Mister
Eric here
Eric
6
Cindy