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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?

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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

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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?

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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

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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?

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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

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Solve a Formula for a Specific Variable

In the following exercises, use the formula d = r t .

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

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Solve for t
when d = 240 and r = 60
in general

t = 4 t = d r

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Solve for t
when d = 510 and r = 60
in general

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Solve for t
when d = 175 and r = 50
in general

t = 3.5 t = d r

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Solve for r
when d = 204 and t = 3
in general

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Solve for r
when d = 420 and t = 6
in general

r = 70 r = d t

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Solve for r
when d = 160 and t = 2.5
in general

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Solve for r
when d = 180 and t = 4.5
in general

r = 40 r = d t

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In the following exercises, use the formula A = 1 2 b h .

Solve for b
when A = 126 and h = 18
in general

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Solve for h
when A = 176 and b = 22
in general

h = 16 h = 2 A b

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Solve for h
when A = 375 and b = 25
in general

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Solve for b
when A = 65 and h = 13
in general

b = 10 b = 2 A h

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

Solve for the principal, P for
I = $ 5,480 , r = 4 % ,
t = 7 years
in general

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Solve for the principal, P for
I = $ 3,950 , r = 6 % ,
t = 5 years
in general

P = $ 13 , 166.67 P = I r t

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

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

t = 2 years t = I Pr

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In the following exercises, solve.

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

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

y = −5 y = 10 5 x 2

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

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

y = 17 y = 5 4 x

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Solve a + b = 90 for b .

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Solve a + b = 90 for a .

a = 90 b

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Solve 180 = a + b + c for a .

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Solve 180 = a + b + c for c .

c = 180 a b

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

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

y = 13 9 x

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Solve the formula −4 x + y = −6 for y.

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Solve the formula −5 x + y = −1 for y.

y = −1 + 5 x

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

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

y = 11 3 x 4

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Solve the formula x y = −4 for y .

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Solve the formula x y = −3 for y .

y = 3 + x

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

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

W = P 2 L 2

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Solve the formula C = π d for d .

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Solve the formula C = π d for π .

π = C d

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Solve the formula V = L W H for L .

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Solve the formula V = L W H for H .

H = V L W

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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 = 5 9 ( F 32 ) to find the Fahrenheit temperature.

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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 = 9 5 C + 32 to find the Celsius temperature.

10°C

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Writing exercises

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

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

Answers will vary.

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Self check

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

This is a table that has three rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can…,” “confidently,” “with some help,” and “no-I don’t get it!” The first column below “I can…” reads “use the distance, rate, and time formula,” and “solve a formula for a specific variable.” The rest of the cells are blank.

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

Questions & Answers

help me understand graphs
Marlene Reply
what kind of graphs?
bruce
function f(x) to find each value
Marlene
I am in algebra 1. Can anyone give me any ideas to help me learn this stuff. Teacher and tutor not helping much.
Marlene
Given f(x)=2x+2, find f(2) so you replace the x with the 2, f(2)=2(2)+2, which is f(2)=6
Melissa
if they say find f(5) then the answer would be f(5)=12
Melissa
I need you to help me Melissa. Wish I can show you my homework
Marlene
How is f(1) =0 I am really confused
Marlene
what's the formula given? f(x)=?
Melissa
It shows a graph that I wish I could send photo of to you on here
Marlene
Which problem specifically?
Melissa
which problem?
Melissa
I don't know any to be honest. But whatever you can help me with for I can practice will help
Marlene
I got it. sorry, was out and about. I'll look at it now.
Melissa
Thank you. I appreciate it because my teacher assumes I know this. My teacher before him never went over this and several other things.
Marlene
I just responded.
Melissa
Thank you
Marlene
-65r to the 4th power-50r cubed-15r squared+8r+23 ÷ 5r
WENDY Reply
write in this form a/b answer should be in the simplest form 5%
August Reply
convert to decimal 9/11
August
Equation in the form of a pending point y+2=1/6(×-4)
Jose Reply
write in simplest form 3 4/2
August
definition of quadratic formula
Ahmed Reply
From Google: The quadratic formula, , is used in algebra to solve quadratic equations (polynomial equations of the second degree). The general form of a quadratic equation is , where x represents a variable, and a, b, and c are constants, with . A quadratic equation has two solutions, called roots.
Melissa
what is the answer of w-2.6=7.55
What Reply
10.15
Michael
w = 10.15 You add 2.6 to both sides and then solve for w (-2.6 zeros out on the left and leaves you with w= 7.55 + 2.6)
Korin
Nataly is considering two job offers. The first job would pay her $83,000 per year. The second would pay her $66,500 plus 15% of her total sales. What would her total sales need to be for her salary on the second offer be higher than the first?
Mckenzie Reply
x > $110,000
bruce
greater than $110,000
Michael
Estelle is making 30 pounds of fruit salad from strawberries and blueberries. Strawberries cost $1.80 per pound, and blueberries cost $4.50 per pound. If Estelle wants the fruit salad to cost her $2.52 per pound, how many pounds of each berry should she use?
nawal Reply
$1.38 worth of strawberries + $1.14 worth of blueberries which= $2.52
Leitha
how
Zaione
is it right😊
Leitha
lol maybe
Robinson
8 pound of blueberries and 22 pounds of strawberries
Melissa
8 pounds x 4.5 = 36 22 pounds x 1.80 = 39.60 36 + 39.60 = 75.60 75.60 / 30 = average 2.52 per pound
Melissa
8 pounds x 4.5 equal 36 22 pounds x 1.80 equal 39.60 36 + 39.60 equal 75.60 75.60 / 30 equal average 2.52 per pound
Melissa
hmmmm...... ?
Robinson
8 pounds x 4.5 = 36 22 pounds x 1.80 = 39.60 36 + 39.60 = 75.60 75.60 / 30 = average 2.52 per pound
Melissa
The question asks how many pounds of each in order for her to have an average cost of $2.52. She needs 30 lb in all so 30 pounds times $2.52 equals $75.60. that's how much money she is spending on the fruit. That means she would need 8 pounds of blueberries and 22 lbs of strawberries to equal 75.60
Melissa
good
Robinson
👍
Leitha
thanks Melissa.
Leitha
nawal let's do another😊
Leitha
we can't use emojis...I see now
Leitha
Sorry for the multi post. My phone glitches.
Melissa
Vina has $4.70 in quarters, dimes and nickels in her purse. She has eight more dimes than quarters and six more nickels than quarters. How many of each coin does she have?
Mckenzie Reply
10 quarters 16 dimes 12 nickels
Leitha
A private jet can fly 1,210 miles against a 25 mph headwind in the same amount of time it can fly 1,694 miles with a 25 mph tailwind. Find the speed of the jet.
Crispy Reply
wtf. is a tail wind or headwind?
Robert
48 miles per hour with headwind and 68 miles per hour with tailwind
Leitha
average speed is 58 mph
Leitha
Into the wind (headwind), 125 mph; with wind (tailwind), 175 mph. Use time (t) = distance (d) ÷ rate (r). since t is equal both problems, then 1210/(x-25) = 1694/(×+25). solve for x gives x=150.
bruce
the jet will fly 9.68 hours to cover either distance
bruce
Riley is planning to plant a lawn in his yard. He will need 9 pounds of grass seed. He wants to mix Bermuda seed that costs $4.80 per pound with Fescue seed that costs $3.50 per pound. How much of each seed should he buy so that the overall cost will be $4.02 per pound?
Vonna Reply
33.336
Robinson
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 cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot?
Imaan Reply
Ivan has $8.75 in nickels and quarters in his desk drawer. The number of nickels is twice the number of quarters. How many coins of each type does he have?
mikayla Reply
2q=n ((2q).05) + ((q).25) = 8.75 .1q + .25q = 8.75 .35q = 8.75 q = 25 quarters 2(q) 2 (25) = 50 nickles Answer check 25 x .25 = 6.25 50 x .05 = 2.50 6.25 + 2.50 = 8.75
Melissa
John has $175 in $5 and $10 bills in his drawer. The number of $5 bills is three times the number of $10 bills. How many of each are in the drawer?
mikayla Reply
7-$10 21-$5
Robert
Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total $23,500? (Round your answer to the nearest tenth of a percent.)
Parker Reply

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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