Shania collected 15 more bottles than Randolph. Together, Shania and Randolph collected 73 bottles. How many bottles did Randolph collect?

Answer 1

Hi Lili,

Let's break down this question! We will use variables to represent each of the people in the problem:

Shania = S

Randolph = R

In total, both Shania and Randolph collected 73 bottles. We can represent that as the equation below:

S + R = 73

Now, we tackle the first part of the question, where you state that Shania collected 15 more bottles than Randolph. We can represent the equation by using Randolph as a variable added with 15 will equal Shania. This means that however many bottles Randolph collected, you can substitute his number into this equation, and add 15 bottles, to get the total number of bottles collected by Shania.

R + 15 = S

Now, we have two equations. Next, we can approach and see how many bottles Randolph has. Well, we can use the second equation and substitute that into the first equation; substitute wherever you see an S for R + 15.

S + R = 73 & R + 15 = S

(R + 15) + R = 73

Now we can look and see that we have common-like terms and simplify the equation to solve for just R; R as in bottles collected by Randolph.

2R + 15 = 73

Subtract 15 on both sides:

2R = 73 - 15

2R = 58

Now divide 2 into both sides so we can isolate R.

R = 58/2

R = 29 bottles

So this means Randolph has a total of 29 bottles. Now we have to check and see how many bottles does Shania have and whether all the bottles add up to the original total of 73 bottles.

Use the second equation from the top of this problem:

R = 29 bottles

R + 15 = S

29 + 15 = S

S = 44 bottles --> This shows that Shania has 15 more bottles than Randolph, so a total of 44 bottles.

Now we have to find if both people have a total of 73 bottles. Let us use the first equation:

S + R = 73

S = 44 bottles

R = 29 bottles

29 + 44 = 73

73 bottles = 73 bottles --> This checks out that both people do have a total of 73 bottles!!

Now to answer your question, how many bottles does Randolph have, well, we solved it earlier and it shows that Randolph has a total of 44 bottles that he has collected!!

Hope this helps you understand how to break down problems that you may encounter in the future!

Answer 2

Let number of bottles collected by Shana = x

number of bottles collected by Randolph = y.

It follows that x = y + 15, and x + y = 73.

Substitute y + 15 for x in the latter equation to get (y + 15) + y = 73. Solve for y, then go back to the equation x = y + 15 to determine x.