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IM Alg1.2.9 Practice: Which Variable to Solve for? (Part2)

A car has a 16-gallon fuel tank.

When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while. How many miles has the car traveled if it has 15 gallons of gas left in the tank?

How many miles has the car traveled if it has 10 gallons of gas left in the tank?

How many miles has the car traveled if it has 2.5 gallons of gas left in the tank?

Write an equation that represents the relationship between the distance the car has traveled in miles, , and the amount of gas left in the tank in gallons, .

How many gallons are left in the tank when the car has traveled 90 miles on the highway?

How many gallons are left in the tank when the car has traveled 246 miles on the highway?

Write an equation that makes it easier to find the the amount of gas left in the tank, , if we know the car has traveled  miles. 

The area A of a rectangle is represented by this formula:

 is the length and  is the width. The length of the rectangle is 5. Write an equation that makes it easy to find the width of the rectangle if we know the area and the length.

Noah is helping to collect the entry fees at his school's sports game.

Student entry costs $2.75 each and adult entry costs $5.25 each. At the end of the game, Diego collected $281.25. Select all equations that could represent the relationship between the number of students, , the number of adults, , and the dollar amount received at the game.

Select all that apply
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is an equation to calculate the volume of a cylinder, , where  represents the radius of the cylinder and  represents its height. Which equation allows us to easily find the height of the cylinder because it is solved for ?

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The data represents the number of hours 10 students slept on Sunday night.

6 6 7 7 7 8 8 8 8 9 Are there any outliers? Explain your reasoning.

The table shows the volume of water in cubic meters, V, in a tank after water has been pumped out for a certain number of minutes.

 Which equation could represent the volume of water in cubic meters after  minutes of water being pumped out?

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A catering company is setting up for a wedding.

They expect 150 people to attend. They can provide small tables that seat 6 people and large tables that seat 10 people. Find a combination of small and large tables that seats exactly 150 people.

Let  represent the number of small tables and  represent the number of large tables. Write an equation to represent the relationship between  and .

Explain what the point  means in this situation.

Is the point  a solution to the equation you wrote? Explain your reasoning.

Which equation has the same solution as ?

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Noah is solving an equation and one of his moves is unacceptable.

Here are the moves he made. Which answer best explains why the “divide each side by  step” is unacceptable?

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Lin says that a solution to the equation  must also be a solution to the equation . Write a convincing explanation about why this is true.