This is a proportion problem. The trickiest part of solving proportions is setting them up correctly. There are as many correct ways to set up a proportion as there are incorrect ways. The key is that there are 4 pairs of associated numbers. And in a proportion, , we have four pairs: the left-side fraction, the right-side fraction, the two numerators and the two denominators. A correct proportion will reflect the associations between the numbers.
In your problem we have two at bat numbers, two home run numbers, two "today" numbers and two "future" numbers. All we have to do is put each pair of numbers from the problem into the pairs of positions in the proportion.
Let's see how this can work. Here are some correct proportions for solving the first of you problems:
Today Future
| |
V V
At bats --> 4885 8059
----- = -----
Home runs --> 351 x
OR
Today Future
| |
V V
Home runs --> 351 x
----- = -----
At bats --> 4885 8059
OR
At Bats Home Runs
| |
V V
Today --> 4885 351
----- = -----
Future --> 8059 x
OR
At Bats Home Runs
| |
V V
Future --> 8059 x
----- = -----
Today --> 4885 351
I hope you get the idea. There are just as many wrong ways to set up the proportion. Here are a couple:
Today Future
| |
V V
At bats --> 4885 x <== Error these are not both at bats
----- = -----
Home runs --> 351 8059 <== Error these are not both home runs
OR
Today Future
| |
V V
At bats --> 4885 8059
----- = -----
Home runs --> x 351
^ ^
| |
| +----- Error: these are not both future numbers
+------------------- Error: these are not both today numbers
Now we will solve the proportion. The one and only time it is correct to use "Cross Multiplication" is when you have a proportion (one fraction equals another)!! We have a proportion so we will use Cross Multiplication to solve. Any of the correct ones will work:
Cross multiplying:
Dividing both sides by 4885:
So the prediction is that at 8059 at bats Albert Pujols will have hit 579 home runs.
For the other problem:
Make sure you understand why this is one of the correct proportions for the second question.
Dividing both sides by 351:
So the prediction is that it will take Albert Pujols 7933 at bats to reach 570 home runs.