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

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Aurelia is driving from Miami to Orlando at a rate of 65 miles per hour. The distance is 235 miles. To the nearest tenth of an hour, how long will the trip take?

Kareem wants to ride his bike from St. Louis to Champaign, Illinois. The distance is 180 miles. If he rides at a steady rate of 16 miles per hour, how many hours will the trip take?

11.25 hours

Javier is driving to Bangor, 240 miles away. If he needs to be in Bangor in 4 hours, at what rate does he need to drive?

Alejandra is driving to Cincinnati, 450 miles away. If she wants to be there in 6 hours, at what rate does she need to drive?

75 mph

Aisha took the train from Spokane to Seattle. The distance is 280 miles and the trip took 3.5 hours. What was the speed of the train?

Philip got a ride with a friend from Denver to Las Vegas, a distance of 750 miles. If the trip took 10 hours, how fast was the friend driving?

75 mph

Solve a Formula for a Specific Variable

In the following exercises, use the formula $d=rt$ .

Solve for $t$
when $d=350$ and $r=70$
in general

Solve for $t$
when $d=240\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}r=60$
in general

$t=4$ $t=\frac{d}{r}$

Solve for $t$
when $d=510\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}r=60$
in general

Solve for $t$
when $d=175\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}r=50$
in general

$t=3.5$ $t=\frac{d}{r}$

Solve for $r$
when $d=204\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}t=3$
in general

Solve for $r$
when $d=420\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}t=6$
in general

$r=70$ $r=\frac{d}{t}$

Solve for $r$
when $d=160\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}t=2.5$
in general

Solve for $r$
when $d=180\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}t=4.5$
in general

$r=40$ $r=\frac{d}{t}$

In the following exercises, use the formula $A=\frac{1}{2}bh$ .

Solve for $b$
when $A=126\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}h=18$
in general

Solve for $h$
when $A=176\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}b=22$
in general

$h=16$ $h=\frac{2A}{b}$

Solve for $h$
when $A=375\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}b=25$
in general

Solve for $b$
when $A=65\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}h=13$
in general

$b=10$ $b=\frac{2A}{h}$

In the following exercises, use the formula I = Prt .

Solve for the principal, P for
$I=\text{}5,480,r=4%,$
$t=7\phantom{\rule{0.2em}{0ex}}\text{years}\phantom{\rule{0.2em}{0ex}}$
in general

Solve for the principal, P for
$I=\text{}3,950,r=6%,$
$t=5\phantom{\rule{0.2em}{0ex}}\text{years}\phantom{\rule{0.2em}{0ex}}$
in general

$P=\text{}13,166.67$ $P=\frac{I}{rt}$

Solve for the time, t for
$I=\text{}2,376,P=\text{}9,000,$
$r=4.4%$
in general

Solve for the time, t for
$I=\text{}624,P=\text{}6,000,$
$r=5.2%$
in general

$t=2$ years $t=\frac{I}{\mathrm{Pr}}$

In the following exercises, solve.

Solve the formula $2x+3y=12$ for y
when $x=3$
in general

Solve the formula $5x+2y=10$ for y
when $x=4$
in general

$y=-5$ $y=\frac{10-5x}{2}$

Solve the formula $3x-y=7$ for y
when $x=-2$
in general

Solve the formula $4x+y=5$ for y
when $x=-3$
in general

$y=17$ $y=5-4x$

Solve $a+b=90$ for $b$ .

Solve $a+b=90$ for $a$ .

$a=90-b$

Solve $180=a+b+c$ for $a$ .

Solve $180=a+b+c$ for $c$ .

$c=180-a-b$

Solve the formula $8x+y=15$ for y.

Solve the formula $9x+y=13$ for y.

$y=13-9x$

Solve the formula $-4x+y=-6$ for y.

Solve the formula $-5x+y=-1$ for y.

$y=-1+5x$

Solve the formula $4x+3y=7$ for y .

Solve the formula $3x+2y=11$ for y .

$y=\frac{11-3x}{4}$

Solve the formula $x-y=-4$ for y .

Solve the formula $x-y=-3$ for y .

$y=3+x$

Solve the formula $P=2L+2W$ for $L$ .

Solve the formula $P=2L+2W$ for $W$ .

$W=\frac{P-2L}{2}$

Solve the formula $C=\pi d$ for $d$ .

Solve the formula $C=\pi d$ for $\pi$ .

$\pi =\frac{C}{d}$

Solve the formula $V=LWH$ for $L$ .

Solve the formula $V=LWH$ for $H$ .

$H=\frac{V}{LW}$

## Everyday math

Converting temperature While on a tour in Greece, Tatyana saw that the temperature was 40 o Celsius. Solve for F in the formula $C=\frac{5}{9}\left(F-32\right)$ to find the Fahrenheit temperature.

Converting temperature Yon was visiting the United States and he saw that the temperature in Seattle one day was 50 o Fahrenheit. Solve for C in the formula $F=\frac{9}{5}C+32$ to find the Celsius temperature.

10°C

## Writing exercises

Solve the equation $2x+3y=6$ for $y$
when $x=-3$
in general
Which solution is easier for you, or ? Why?

Solve the equation $5x-2y=10$ for $x$
when $y=10$
in general
Which solution is easier for you, or ? Why?

## Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

the proudact of 3x^3-5×^2+3 and 2x^2+5x-4 in z7[x]/ is
?
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?
44.19%
Scott
40.22%
Terence
44.2%
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?
paul
What is the lcm of 340
Yes
Cherokee