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Algebra II : Solving Equations

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Example Question #212 : Equations

Jason has $ 400 and spends $ a day. Paul has $ and adds $ a day. When will they have the same amount of money?

Possible Answers:

Correct answer:

Explanation:

Let's set-up an equation.

400-2x=50+5x represent time it will take for them to have the same amount of money. By adding on both sides, subtracting on both sides later, and finally dividing by on both sides, we get x=50 days.

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Example Question #213 : Equations

A cat can dig a hole at a rate of feet per day. This cat starts digging for one week. A dog comes along and watches the cat dig and joins along. The dog digs for feet per day. If a buried treasure is 2512 feet below surface, how long has the cat dug until they both reach the trasure?

Possible Answers:

Correct answer:

Explanation:

Let's set-up an equation.

16*7+(16+24)x=2512 16*7 represents the cat's head start and how much the cat started digging. The last part represents the sum of the rates of both animals since they start working together. is the number of days.

112+40x=2512 Subtract 112 on both sides.

40x=2400 Divide on both sides.

x=60 days

Our answer is not done since it's asking about the cat. So we add and to get days.

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Example Question #213 : Equations

Possible Answers:

Correct answer:

Explanation:

Let's set-up an equation.

112+40x=2512 Subtract 112 on both sides.

40x=2400 Divide on both sides.

x=60 days

Our answer is not done since it's asking about the cat. So we add and to get days.

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Example Question #214 : Equations

To convert Celsius to Fahrenheit temperatures, you multiply Celsius by $\frac{9}{5}$ and then add . What is the Celsius temperature when the Fahrenheit temperature is ?

Possible Answers:

Correct answer:

Explanation:

Our equation looks like: $\frac{9}{5}C+32=F$ By subtituting , we have $\frac{9}{5}C+32=-40$ Subtract on both sides.

$\frac{9}{5}C=-72$ Multiply $\frac{5}{9}$ on both sides.

C=-40

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Example Question #215 : Equations

A lion spots a deer 288 meters away. The lion chases the deer at meters/second. At the same time, the deer runs away at a speed of meters/second. How long will it take when the two animals are meters apart?

Possible Answers:

40 seconds

16 seconds

12 seconds

Correct answer:

16 seconds

Explanation:

Let's set-up an equation.

288+22x-36x=64 As time passes, the deer has the head start and its distance will be 22x+288 . Since the lion's rate is faster and we want the differences of their distances traveled, we subtract the distance the deer went and lion's distance which is 36x .

288-14x=64 Subtract 288 on both sides. Since 288 is greater than and is negative, our answer is negative. We treat as a subtraction problem.

-14x=-224 Divide on both sides. When dividing with another negative number, our answer is positive.

x=16 seconds

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Example Question #215 : Equations

Possible Answers:

40 seconds

16 seconds

12 seconds

Correct answer:

16 seconds

Explanation:

Let's set-up an equation.

288-14x=64 Subtract 288 on both sides. Since 288 is greater than and is negative, our answer is negative. We treat as a subtraction problem.

-14x=-224 Divide on both sides. When dividing with another negative number, our answer is positive.

x=16 seconds

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Example Question #216 : Equations

Ellen is swimming in the ocean 250 meters from the beach. She screams for help and starts swimming towards the shore at a speed of 0.8 meters/second. Twenty seconds later, Joe starts rowing a boat toward her at a rate of 2.2 meters/second. How far has Joe rowed when he meets Ellen?

Possible Answers:

124.36

171.6

76.8

96.8

Correct answer:

171.6

Explanation:

Let's set-up an equation.

0.8*20+(0.8+2.2)x=250 Ellen has the head start which is represented by 0.8*20 . Then, Ellen and Joe go at different rates but at the same time which is represented by . represents time.

16+3x=250 Subtract on both sides.

3x=234 Divide on both sides.

x=78 Then we need to multiply that by 2.2 since we are looking for the distance Joe went. Our answer is 78*2.2 or 171.6 miles.

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Example Question #217 : Equations

Ellen is swimming in the ocean 500 meters from the beach. She screams for help and starts swimming towards the shore at a speed of 1.6 meters/second. Twenty seconds later, Joe starts rowing a boat toward her at a rate of 4.4 meters/second. How far has Joe rowed when he meets Ellen?

Possible Answers:

278.2

375.2

343.2

178.2

Correct answer:

343.2

Explanation:

Let's set-up an equation.

1.6*20+(1.6+4.4)x=500 Ellen has the head start which is represented by 1.6*20 . Then, Ellen and Joe go at different rates but at the same time which is represented by . represents time.

32+6x=500 Subtract on both sides.

6x=468 Divide on both sides.

x=78 Then we need to multiply that by 4.4 since we are looking for the distance Joe went. Our answer is 78*4.4 or 343.2 miles.

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Example Question #218 : Equations

Joe and Cara are making meatballs. They have 1200 to make. Joe can make meatballs a minute while Cara can make meatballs a minute. After working together for forty-two minutes, Cara had to leave leaving Joe to finish the rest. How long does Joe take to finish the rest?

Possible Answers:

Correct answer:

Explanation:

Let's set-up an equation.

(12+8)42+12x=1200

(12+8)42 represents how many meatballs they make together

12x represents the number of meatballs Joe needs to make with being time

840+12x=1200 Subtract 840 on both sides.

360=12x Divide on both sides.

x=30 minutes

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Example Question #81 : Solving Equations

A tank can fill a swimming pool in two hours. A hose can fill the same swimming pool in three hours. How long will it take in hours if both the tank and hose fill the swimming pool at the same time?

Possible Answers:

$2\frac{1}{2}$

$1\frac{1}{6}$

$1\frac{1}{5}$

$1\frac{1}{2}$

Correct answer:

$1\frac{1}{5}$

Explanation:

Let's set-up an equation.

$\frac{x}{2}+\frac{x}{3}=1$

represents the time they will take together and represents the job both the tank and hose finish as a whole

Find the common denominator and add the fractions. $\frac{5x}{6}=1$ . Cross-multiply.

5x=6 Divide on both sides.

$x=\frac{6}{5}or 1 \frac{1}{5}$ hours

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Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #212 : Equations

Example Question #213 : Equations

Example Question #213 : Equations

Example Question #214 : Equations

Example Question #215 : Equations

Example Question #215 : Equations

Example Question #216 : Equations

Example Question #217 : Equations

Example Question #218 : Equations

Example Question #81 : Solving Equations

All Algebra II Resources

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