An architect has a scale drawing of an addition that is to be added to a house with a scale of 1 inch : 2 feet. If the drawing is 6 inches by 10 inches, how big is the addition to the house going to be?

Hey! Let me help you on this one.

In order for us to solve this problem, we will be needing to form a ratio just like the ones the question provides to us. In case you don't quite understand how to do it, don't fret and watch me explain it. I will also be attaching an image with all the work shown in case you need extra help.

As we know, the scale of the house is 1 inch : 2 feet. First of all, let's balance the unit sizes by converting 2 feet into inches, thus making the problem much easier.

One foot is 12 inches, meaning that two feet should be two times more than 12 inches.

[tex]12(2)=24[/tex]

Great! We can now form the balanced ratio. It is going to be 1 inch : 24 inches. Now, let's form an actual ratio with plugged in unknown variable in order for us to solve for it.

[tex] \frac{1}{24} : \frac{6}{x} [/tex]

According to the ratio, our numerator on the right side is six time bigger than numerator on the left side, meaning that our denominator on the right side is six times bigger than denominator on the left side as well. Keeping this in mind, let's solve for it.

[tex]24(6)=144[/tex]

Awesome! One of the sides is 144 inches. We are left with only one side which is 10 inches on the scale. Let's form the same ratio and solve for it.

[tex] \frac{1}{24} : \frac{10}{x} [/tex]

Just like we did in our last step, let's multiply the left denominator with the right numerator.

[tex]24(10)=240[/tex]

We now know values of two sides, and we can set it as our answer.

Answer:144 by 240 inches is the size of the house.