## Bertha’s Tax

Some years back, when sales tax was exactly 4%, Bertha priced a cat toy in dollars and cents so that when she sold it in her store, which is cleverly named Bertha’s Pet Store, the price plus the tax came out to an exact number of dollars, with no rounding at all. What is the smallest possible price for which this works? (Note: 96 cents for a price is no good because you have to round the tax to the nearest penny. 4% of \$0.96 isn’t 4 cents.)

## Product with Absolute Value

If x is a real number, then for what values of x is the quantity (1 – |x|)(1 + x) a positive number?

• x < 1
• x = 1
• x > 1
• x < -1
• x < -1 or -1 < x << 1

## Continued Fraction with 1’s and 3’s

What is the value of this fraction that continues forever in the same pattern? (You’ll want the quadratic formula.)

## Stella’s Bookshelves

As we all know, Stella studied piano with the renowned Nadia Boulanger in Paris after World War II. In Amsterdam, in her studio, she has three shelves with books of four-hand piano music that she often plays with her husband Graziano (who needs to practice more). The top shelf contains 1/6 of all the scores. The middle shelf contains more than 2/5 of the scores, and the bottom shelf contains only four scores (but they’re thick ones). What is the smallest total number of scores that she might have on all three shelves?

## Maumee Limerick

I have a friend out in Maumee
Whose age has the last digit 3.
The square of the first
Is her whole age reversed,
So what must the lady’s age be?