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How would you solve a problem of this type using Microsoft Excel?

A bat and ball cost a dollar and ten cents. 
The bat costs a dollar more than the ball. 
How much does the ball cost?

(The answer is that the bat costs $1.05 and the ball costs $0.05.)

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migrated from math.stackexchange.com Jun 14 '12 at 12:07

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Why on earth would you use Excel for that? –  Hans Lundmark Jun 14 '12 at 11:41
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Perhaps a more pertinent question is "Why would you work it out in MS Excel?" –  Peter Taylor Jun 14 '12 at 11:42
    
@ Hans Lundmark, Why not? –  oshirowanen Jun 14 '12 at 11:42
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I'm reopening this... it seems like an odd (not-a-real) question but Kaze wrote a great answer about goal seek so with some editing I think it can be salvaged –  Joel Spolsky Jun 15 '12 at 2:58
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I think it's a really good question-the specific example is easy, but the concept has quite a bit of potential for solving complex problems. I often try and simplify examples to make sure they work before applying them to real-world complexities. –  dav Jun 15 '12 at 13:40
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3 Answers 3

up vote 5 down vote accepted

Another way using Goal Seek:

Enter the formula for the price of a bat in one cell (BALL_PRICE + 1.00), and the total in another (BALL_PRICE + BAT_PRICE). In my example below, A2 contains the formula for the price of a bat, and C2 contains the total:

enter image description here

Open Data > What-If Analysis > Goal Seek and set it up this way:

enter image description here

You should get this after clicking OK:

enter image description here

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This is a nice, easy solution that doesn't require you to do the algebra by hand first (which was the best I could figure). –  dav Jun 15 '12 at 13:39
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Bat price 1

Ball price 0.1 (=1.1 - bat price)

Difference 0.9 (=bat price - ball price)

Error 0.1 (=1.0-difference)

Now use goal seek to set error to 0 by changing bat price.

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As @Hans said, there's no need for Excel here. Let x be the price of the bat and y be the price of the ball. Since the two together cost $1.10 we have (in cents) x + y = 110. Since the bat costs a dollar more than the ball, we have x = y + 100.

The second equation allows us to replace x in the first, so (x) + y = 110 becomes (y + 100) + y = 110 so we find 2_y_ + 100 = 110 and subtracting 100 from both sides gives 2y = 10 so y = 5 so the ball costs 5 cents and hence, since the two prices total 110 we find that the bat must cost 105.

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