SAT Ratios, Rates & Proportions Question 20 | Free SAT Prep | Aniko

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Question 20·Medium·Ratios, Rates, Proportional Relationships, and Units

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A car travels 180 miles on 6 gallons of gasoline. At this rate, how many gallons of gasoline would the car use to travel 300 miles?

For SAT ratio and rate questions like this, quickly turn the information into a simple rate (such as miles per gallon) by dividing, then use that rate to scale up or down. Alternatively, set up a clear proportion (known ratio = unknown ratio) and solve for the missing value with one or two clean algebra steps. Always check that your answer makes sense: if the distance increases, the fuel used should increase by the same factor.

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Identify what is being asked

You are given how far the car travels using 6 gallons. The question asks how many gallons are needed for a different distance (300 miles). Think about the relationship between miles and gallons.

Find a rate first

Try to find how many miles the car travels per 1 gallon of gasoline. You can do this by dividing the miles by the gallons given.

Scale up using the rate

Once you know how many miles the car goes on 1 gallon, use that to figure out how many gallons are needed for 300 miles. Ask yourself: 300 is how many times that 1-gallon distance?

Alternative: Set up a proportion

You can also write a proportion: $\frac{180\text{ miles}}{6\text{ gallons}} = \frac{300\text{ miles}}{x\text{ gallons}}$ and solve for $x$ .

Desmos Guide

Compute the unit rate and gallons in Desmos

In Desmos, type 300*(6/180) to model "300 miles times gallons per mile" based on the original ratio. The numerical output that Desmos gives is the number of gallons needed for 300 miles at the same rate.

Step-by-step Explanation

Find the unit rate (miles per gallon)

We know the car travels 180 miles using 6 gallons of gasoline.

Compute the miles per gallon:

\text{miles per gallon} = \frac{180}{6} = 30

So the car travels 30 miles for each gallon of gasoline.

Use the unit rate to find gallons for 300 miles

Now we want to know how many gallons are needed for 300 miles if the car goes 30 miles per gallon.

Set up the equation using the rate:

\text{gallons needed} = \frac{300\text{ miles}}{30\text{ miles per gallon}}

Then simplify this fraction.

Compute and choose the answer

Now do the division:

\frac{300}{30} = 10

So, the car would use 10 gallons of gasoline to travel 300 miles. That corresponds to choice C.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation