My first impulse was to do as the writer suggested and assign 100 to the bat and 10 to the ball...’till I worked the math. Boy did I feel stupid. And this is pretty much the extent of my algebra skills...sorry to say!
No need to go through all those permutations. You’ve already subtracted $1 from the total, leaving 10¢; therefore whatever the smaller price is, the larger price is $1 larger, $1.05 being $1 larger than 5¢. Just a riddle to throw people’s thinking off, like “Who is buried in Grant’s Tomb?” or “What’s the opposite of ‘Not In’?” (some people will answer “Out” when caught off-guard; sharp-minded people will answer “Not out”). Math that really gives me headaches is (in calculus) trigonometric substitution and integration by parts; the reason I mentioned physical chemistry earlier in this thread is because AFAICS, far more advanced math is needed to learn it (differential equations and beyond), but many colleges require only calculus II and math beyond that is merely elective according to the degree program . . .
Just do a system of equations. Let x = ball and y = bat. Now:
y = x + 1
x + y = 1.10
Subtract x from both sides of the first equation to give you: -x + y = 1, and then add this equation to the second equation:
-x + y = 1
x + y = 1.10
2y = 2.10
Solve for y:
y = 1.05
Plug the y value back into one of the equations to solve for x:
x + 1.05 = 1.10
x = 1.10 - 1.05
x = .05