Help w/ 'Bubba bought several items, all the same price....'

[evergreens]

Bubba bought several items, all the same price. The number of items was equal to the cost of each in cents. The change that Bubba received from $10 was $1 and 7 coins totaling less than $1. How much did each item cost?

 

[soroban]

Re: Help

Hello, evergreens!

Did you try anything?

Bubba bought several items, all the same price.
The number of items was equal to the cost of each in cents.
The change that Bubba received from $10 was $1 and 7 coins totaling less than $1.
How much did each item cost?

If the change from $10 was a dollar and some change,
. . Bubba must have spent between 800 and 900 cents.

Since the he bought \(\displaystyle x\) items at \(\displaystyle x\) cents each, he paid \(\displaystyle x^2\) cents.

The only square in the 800's is: \(\displaystyle \,29^2\,=\,841\)

Bubba bought 29 items at 29¢ each.

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All that stuff about the seven coins is just smoke and mirrors,
. . included to confuses us. .(Did it work?)

His change was $1.59 . . . a dollar bill and seven coins:
. . two quarters, one nickel and four pennies.