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

 Page 4 / 4

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?

#### Questions & Answers

what is the answer for this 3×9+28÷4-8
315
lashonna
how do you do xsquard+7x+10=0
What
(x + 2)(x + 5), then set each factor to zero and solve for x. so, x = -2 and x = -5.
bruce
I skipped it
What
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
25%
Melissa
25 percent
Muzamil
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
Finally 👍
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
thanks melissa
Jeorge
950000-713500 *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.
6t+3
Melissa
6t +3
Bollywood
Tricia got a 6% raise on her weekly salary. The raise was $30 per week. What was her original salary? Iris Reply 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
28.50
Toi
thanks
Jeorge
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? Valeria Reply 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?
WY need
Fernando
How did you get $750? Laura Reply if y= 2x+sinx what is dy÷dx formon25 Reply does it teach you how to do algebra if you don't know how Kate Reply 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
the definition of length
literal meaning of length
francemichael
exact meaning of length
francemichael
exact meaning of length
francemichael
how many typos can we find...?
5
Joseph
In the LCM Prime Factors exercises, the LCM of 28 and 40 is 280. Not 420!