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.)
Set 06
Quadratic to Multiply & Factor
Given (y + 1)(2y – 3) = 25, then y = what? (Don’t guess!)
Product with Absolute Value
If x is a real number, then for what values of x is the quantity
- x < 1
- x = 1
- x > 1
- x < -1
- x < -1 or -1 < x << 1
Equation with Fractions
Find a number that is 58 more than the sum of its third, tenth, and twelfth parts.
Number of Positive Integer Solutions
The number of solution pairs in positive integers of the equation 3x + 5y = 501 is:
- 33
- 34
- 35
- 100
- none of these
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.)
Triple Ratio
is equal toKumquats
If x dozen kumquats sell for y dollars, write a formula for the cost of exactly z kumquats. Check your formula by plugging in some easy numbers.
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?
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?