Learn about Applications of Two-Step Equations Two-step equations: So in this problem it states that this camp area already has 32 camp sites around the lake. Now the park wants to add an equal number of sites to each of 30 acres. They want a total of 302 campsites. How many campsites will they add to each acre? All right, so to determine the number of campsites to be added to each acre, we need to follow these steps. So the first step we need to do is we need to write an equation. So what we need to find out is the total number of sites. So we’re going to take the number of the acres times the new campsites per acre plus the number of old sites and that will give us the total number of sites. So our equation is the number of acres x the new campsites per acre plus the number of old sites and this will give us our total number of sites. Now, let’s let P represent the number of campsites to be added to each acre. We’re going to say the new campsites per acre are P. Now the total number of acres, our total number of acres is 30. So we have 30 acres. So this will be the number of acres will be 30. Now the total number of old sites from out problem is 32, we have 32 campsites that they already have. So the old sites are 32. And the total number of sites they want a total of 302 campsites. So the total number of site is 302. So let’s go ahead and just plug this in. So we have 30 x p + 32 = 302. So what we’re going to do is to make this easier as we’re just going to multiply 30 x p, so we get 30p + 32 = 302. All right, now we have our equation. So our second step is we need to isolate the variable. So our variable is p. So we need to isolate. So we’re going to use inverse operation to isolate the variable. Subtraction is the inverse of addition, so if we subtract the same number from both sides, the equation will still be true. So when we isolate variables, we use inverse operation. So if you add, if it’s adding you’re going to subtract. If you are multiplying you’re going to divide and vice versa. So we have our equation 30p + 32 = 302. So the first thing we’re going to do is we’re going to subtract 32 from both sides. So I’m going to take, subtract my 32 from both sides. So when I do that, I’m left with 30p on this side and 302 – 32 is 270. So now I’m left with 270 on this side, on the other side. Now, we’re going to continue and isolate the variable. So now here we’re multiplying, right? So if we multiply division is the inverse of multiplication, so what we’re going to do here is we’re going to divide both sides by 30. So I’m going to divide 30p by 30 and I’m going to divide 270 by 30. So when I do that I get p by itself and 270/30 is 9. So p = 9. Now, let’s check to make sure our answer is correct. So here I’m going check my answer. So to check I need to see 30—I’m going to take my equation 30p + 32 = 302. So I’m going to take my original equation and now I’m going to substitute 9 for p. So I’m going to say 30 x 9 + 32 should equal 302. So 30 x 9 is 270 + 32 = 302 and 270 + 32 = 302 =302. So since both sides of the equation are the same the answer is correct. Therefore, our answer nine is correct. So the new campsites per acre, how many campsites will they need for each acres is 9. They will need 9 campsites for each acre. All right, things to remember and to keep in mind, is that a two-step equation takes two steps to solve. So for example when we had 30 x p + 32 = 302 is a two-step equation. Now because we had to multiply 30, right? So the first then the steps to follow to solve these two-step equations is our first step is to write our equation and then the second one is to use the inverse operation to isolate your variable. Remember that inverse operation is the opposite, so if you add the inverse operation is subtract. If you multiply the inverse operation is divide, and then you continue to isolate the variable using multiplication or division.