Just because

I hate simple problems like these, because once you jump to the wrong conclusion it's really hard to get the right answer:

1) A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?

2) If it takes 5 machines 5 min to make 5 widgets, how long would it take 100 machines to make 100 widgets?

3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake,
how long would it take for the patch to cover half of the lake?

I'm certain the answer to 1) is five cents, and 3) is 47 days. But I can't even begin to guess how to figure out the answer for 2).

Little help?

I agree, you're correct on 1 and 3. I believe the answer to 2 has to be 5 minutes. Well figured, btw; I had to really fight not to say $1.00 and $.10 cents, which I suppose is the point.

1 machine takes 5 minutes to make 1 widget. Multiply from there. That they did 5 machines was a distractor.

Another thing: I'm lousy at math, yet I grasp the value of zero easily on both sides of the decimal point, which many people seem to struggle with.

There's a saying in Spanish to denote something worthless which translates as "A zero to the left." Sure, the number 000001 = 1 all those zeroes to the left have no value, but 1000<>1. On the other side of the decimal point, however, the zeroes to the left are valuable and those to the right don't count. Thus the number 0.90000 = 0.9, but 0.009 <> 0.9

At work to determine margins we usually divide by a fraction. Thus cost/0.7=sale price. Ok? But if I say "The cost divided by point seven equals price," many people "correct" me and say "You mean by point seventy." They seem to think point seven = 0.07. But point seven is right, as 0.7 = 0.70000000000 with an infinity of zeroes if you like.

What gives?

And yes, sometimes after being "corrected" I'll say something like "No, I meant point seven million." Usually I get blank stares in return.

It takes 5 machines 5 minutes to make 5 widgets.

If you had 10 machines, I would expect it to take 2.5 minutes to make 5 widgets, or in 5 minutes they could complete 10 widgets.

So, it would take 100 machines 5 minutes to make 100 widgets.

It is a different way to reach the 1 machine 5 minutes 1 widget answer.

Quote: Dalex64

So, it would take 100 machines 5 minutes to make 100 widgets.

It is a different way to reach the 1 machine 5 minutes 1 widget answer.

I thought of that, but it felt wrong.

I think it's because long ago I read one that went, more or less, "If one and a half chickens lay one and a half eggs in one and a half days," and I forget how it ends, but the answer made no sense to me.

Quote: Nareed

2) If it takes 5 machines 5 min to make 5 widgets, how long would it take 100 machines to make 100 widgets?

Let x = time required for one machine to make one widget.

We're given 5*5*x = 5
x = 0.2.

Let t be the answer to the question at hand.

100*t*0.2 = 100
t=5

So five minutes.

It really helps to learn to write equations.
B=cost of a bat
b=cost of a ball
(1) B=b+$1
(2) B+b=$1.10
substitute equation (1) into equation (2)
b+$1+b=$1.10
2*b=$1.10-$1
2*b=$0.10
b=$0.05

Quote: Wizard

Let x = time required for one machine to make one widget.

When I hear math guys say "Let x be yadda, yadda," I can't help but think they're channeling their inner deity and letting the answer be whatever they want :)

Quote: Pacomartin

It really helps to learn to write equations.

After jumping to the wrong answer, $1 and $0.1, I realized there are two variables and not one, therefore you need two equations and not one. I did learn simultaneous equations in high school, even with three variables (usually x, y and z). I do not recall how to solve them.

But like the FB meme said "Somehow I've managed to survive another day without using Algebra." :)