240 real miles is represented by 3 map inches, making this a ratio of  real miles per map inch. 

Therefore, one and three-fourths inches represents

 miles, the distance between Charlesville and Petersburg.

The ratios that are set equal to each other in a proportion must compare the same quantities in the same order. 

In each ratio, we can put number of map inches in the numerator and the number of actual miles in the denominator.

One ratio is two map inches to twenty-five actual miles (the map scale); this ratio is .

The other ratio is eight map inches to  actual miles (the distance between Pierce Springs and Buchanan Falls); this ratio is .

The proportion statement that sets these equal to each other is , and is therefore the correct choice.

Since this is a proportion, you can cross-multiply. Once you do that, the left side is Your right side is . Set those equal to each other. Then, combine like terms. Subtract from both sides so that the equation is now . Divide both sides by Your answer is

The ratio of ounces of cola to ounces of grape soda in the initial mixture can be expressed as . It must be equal to that of liters of cola to liters of grape soda in the mixture Michelle will make for the party, which, since the number of liters of grape soda is unknown, is . Set these equal and solve for :

Set the cross-products equal to each other:

Michelle will use  liters of grape soda in the final mixture.

What do we know? We know that there are 20 chips in the bag, and we know that Robert has eaten 8 of them. Thus, we can calculate that there are  chips remaining. Of this remaining, Jeff has eaten 2 parts and Paul has eaten 1 part: that's 3 parts, so let's calculate how many chips constitute each part:

So, each part is equal to 4 chips.

Jeff has eaten 2 parts, so  gives us our answer.

To solve this problem we can make proportions.

We know that , and we can use  has our unknown. 

Next, we want to cross multiply and divide to isolate the  on one side. 

The  will cancel and we are left with 

To solve this problem we can make proportions.

We know that  and we can use  as our unknown. 

Next, we want to cross multiply and divide to isolate the  on one side. 

The  will cancel and we are left with 

To solve this problem we can make proportions.

We know that  and we can use  as our unknown. 

Next, we want to cross multiply and divide to isolate the  on one side. 

The  will cancel and we are left with 

To solve this problem we can make proportions.

We know that  and we can use  as our unknown. 

Next, we want to cross multiply and divide to isolate the  on one side. 

The  will cancel and we are left with 

To solve this problem we can make proportions.

We know that  and we can use  as our unknown. 

Next, we want to cross multiply and divide to isolate the  on one side. 

The  will cancel and we are left with