during his career, hank aaron hit 37 more home runs than babe ruth hit during his career.together they hit 1,501 home runs.how many home runs did babe ruth hit?
how many home runs did babe ruth hit
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Let a = number of home runs Hank Aaron hit
Let r = number of home runs Babe Ruth hit.
From the first sentence we know a = r + 37
From the second sentence we know that a + r = 1501
Since a = r + 37, we then have:
(r + 37) + r = 1501
2r + 37 = 1501
2r + 37 - 37 = 1501 - 37
2r = 1464
2r/2 = 1464/2
r = 732, and
a = r + 37 = 732 + 37 = 769
So the answer to the stated problem is that Babe Ruth hit 732 home runs and Hank Aaron hit 769.
Neither of those numbers is historically correct, however. Babe Ruth hit 714 home runs and Hank Aaron hit 755 home runs in their respective Major League careers.
Let's subtract 37 from both sides...
Let's divide both sides by 2...
Ok, so we need to start by figuring out what they're telling us. Hank Aaron and Babe Ruth hit a total of 1,501 home runs over their careers. Hank Aaron hit 37 more than Babe Ruth. We're looking for how many home runs Babe Ruth hit.
Next we need to translate the English into Math. If we use H for Hank and B for Babe, we get:
H + B =1,501 and H=B+37. A system of equations!
Then we replace H in the first equation with the second equation:
Now we solve for B:
2B+37=1,501 (add the B's together)
2B=1,464 (subtract 37 from 1,501)
B=732 (divide 1,464 by 2)
And that's it! Babe Ruth hit 732 home runs during his career.