Multi step equation

Question

Walt bought a new unique guitar (strings included) and an additional set of strings because he plays hard a tends to snap them often. In the middle of his guitar solo, you could hear 3 strings snap over the sound of his voice yelling, "I wanna rock!" Walt's new guitar was not a typical 6 string guitar, in fact, when his strings snapped he was only left with 2/3 of the original strings.

He replaced the broken strings and cranked up the song "Free Bird" by Lynard Skynard on his airpods to get ready for his next jam.

Walt has another older unusual guitar that has 7 less than twice the number of string on his new guitar (Walt is an unusual guy and collects unusual guitars). How many strings are on each of Walt's wild guitars if the total number of strings on the two guitars is 1953 less than the year was Free Bird released?

Answer 1

There's a lot of information here! First we should pick out what we know about each guitar to start.

New guitar: 3 strings snapped, then he was left with 2/3 the original strings. If we say x is the original number of strings, then he has x-3 strings after some strings snapped, or x*2/3 strings.

Now we can set x-3 = x*2/3

x-x*2/3 = 3

x*1/3 = 3

x = 9

We now know the new guitar had 9 strings to start!

Old guitar: 7 less strings than twice the number of the new guitar's strings. As an equation, that's

2(# strings on new guitar) - 7 = 2(9) - 7 = 11. So the old guitar had 11 strings.

We now know the number of strings on both the old guitar and the new guitar, and don't even need the last piece of information! If we want to use it to verify our answer, though, we can see that since Free Bird was released in 1973:

9 + 11 = 1973 - 1953

20 = 20

So that last piece of information is consistent with the answer we already have.