math teaser

[lotus776]

Check this out:

Bethani walks into a store and buys four items, each item priced differently. As she leaves the store, she notices that the total (sum) of all four items is the same as the product of the same four items, which is $7.11/ Ignoring sales tax, what was the individual price of each item?

good luck

-Brent

[theweatherman]

bethani is a tool for spelling her name with an I

$1.20, $1.25, $1.50, and $3.16

[lotus776]

how did you solve this? can you please show me your work?

thanks
-Brent

I don't think there is an algebraic way to completely solve the problem.

You can start with the following. (assuming costs in cents)

w*x*y*z = 711000000
w+x+y+z = 711

Finding factors of 711
711 = 3*3*79

w*x*y*z must be divisible by 3,9,and 79

At this point you can say one of the costs should be $0.79 or a multiple of that. When you divide $7.11 by $0.79 you get a whole number (9) Dividing by $1.58 you get 4.5, and dividing by $3.16 you get 2.25. This suggests that the other 3 prices are multiples of 5 cents.

At that point it's trial and error or using some kind of solver function in a spreadsheet or calculator.