SOLUTION: Albert Pujols is hitting 351 home-runs in 4885 at-bats. Alex Rodriguez is hitting 570 home-runs in 8059 at-bats. At Albert Pujols rate, how many home-runs will he have when he reac

Algebra ->  Proportions -> SOLUTION: Albert Pujols is hitting 351 home-runs in 4885 at-bats. Alex Rodriguez is hitting 570 home-runs in 8059 at-bats. At Albert Pujols rate, how many home-runs will he have when he reac      Log On


   

Question 202910: Albert Pujols is hitting 351 home-runs in 4885 at-bats. Alex Rodriguez is hitting 570 home-runs in 8059 at-bats. At Albert Pujols rate, how many home-runs will he have when he reaches 8059 at-bats? How many at-bats will it take him to reach 570 home-runs?
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
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, a%2Fb+=+c%2Fd, 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:
4885%2F351+=+8059%2Fx
Cross multiplying:
4885%2Ax+=+351%2A8059
Dividing both sides by 4885:
x+=+%28351%2A8059%29%2F4885+=+579.0601842374616172
So the prediction is that at 8059 at bats Albert Pujols will have hit 579 home runs.

For the other problem:
4885%2F351+=+x%2F570
Make sure you understand why this is one of the correct proportions for the second question.
4885%2A570+=+351%2Ax
Dividing both sides by 351:
%284885%2A570%29%2F351+=+x
7932.9059829059829060+=+x
So the prediction is that it will take Albert Pujols 7933 at bats to reach 570 home runs.