 Here's another puzzle I saw yesterday that I still don't truly understand. If you buy a bat and a ball for $1.10, the bat costs exactly 1 pound more than the ball. How much does the ball cost? Joseph says my original answer was that $1.10-1 equals $1, so the ball must cost, but that would mean the ball would only be 0.9 pounds. If the bat would be 0.9 pounds, so the way you would do it, so the way you do it is this, a ball and a bat, a ball plus a bat, costs $1.10. Bat minus ball equals $1, the cost of the bat minus the ball costs $1, so all you got to do is substitute, so I'm going to take this, so this is your first equation, this is your second equation. Always remember this, the number of variables you have, that's how many equations you need to be able to solve a problem. So if you have one unknown, you need one equation to solve it. If you have two unknowns, you need two equations to solve it. Three unknowns, three equations, et cetera, et cetera, et cetera. So you can just bring this over, go minus ball, okay, now the bat is now 1.0 plus minus the ball, minus the ball. And what you can do is, that's the same bat as this, right, so you can take this and sub it in for the bat. So sub 2 into 1, equation 2 into 1, because this is our modified equation 2, right, now you got a ball plus 1.0 minus, what, I'm doing something wrong here, bat, oh, because I'm indignalling, this becomes a plus, right, if the ball comes over, that's a negative, that's a plus. Plus a ball is equal to 1.10. I usually use x and y variables, but I'm using this because if this was a bat and a glove, I would put B for bat and G for glove, but they're both BBs, right, bat, BA, BA, they're both BA. Yeah, thank you anti-socialist behavior. So this becomes 1.0 plus 2 balls is equal to 1.01, because a ball plus a ball is 2 balls, right, grab this guy, bring it over, minus 1.0, so 2 balls is equal to 0.1 and then divide by 2, divide by 2, so ball is equal to 0.05, that's how much the ball costs, and the bat would be, therefore, the bat would be 1.1 minus 0.05, which equals 1.05, that's how much the bat would cost. You notice I didn't write down as Captain Ranger, first time chat, hey Chicho, been following your content from France, Salutations France, and never had a chance to come by and thank you for your outstanding work out there. You guys enjoy the math, need those quiet a lot in product design myself, cheers. You use those quite a lot in product design, myself cheers. Cheers Ranger, thank you very much Captain Ranger for popping in from France, Salutations, bonjour, bonjour. I took French in high school, but I don't remember any of it, I cheated most of it, cheated most of the way through, and this is by the way, this is a common problem that you encounter, one of the generic problems that they give in high school anyway, or as a puzzle, because it's instinctive, people say oh, something costs 1.1, and one has to be a dollar more than the other, and this one costs that, how much is that, oh it's a dollar, no it's not, or a pound, it's not.