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Problem of the Week Archive
Love is in the Air – February 13, 2017
Problems & Solutions
Valentine’s day is this week and in the U.S. over 110 million roses will be
sold and delivered between February 13th and February 15th. Between
those dates, the average cost of a dozen florist-arranged, long-stemmed
roses is $73, according to the Society of American Florists, compared to
$59 average for all other dates during the year. How much more money
do florists make selling 110 million roses over these three days than
selling the same amount other days of the year? Express your answer to
the nearest dollar.
The difference in cost per dozen during this peak time is $73 – $59 = $14. This means that selling 110 million roses,
florists will make $14 × 110,000,000 ÷ 12 ≈ $128,333,333 more over these three days than selling the same amount
other days of the year.
What is the percent increase in cost of a rose, based on the information from
the previous problem? Express your answer to the nearest percent.
The percent increase in cost per rose will be the same as the percent increase per dozen. Since
the price went up $14 from the original $59, the percent increase is 14/59 × 100 ≈ 24%.
Martin wants to make a heart shaped card for his valentine. Martin is in Geometry and loves
constructing geometric shapes, so he decides to make his heart using two semicircles and one
equilateral triangle. The semicircles are tangent to each other and their diameters lie along one edge
of the equilateral triangle. If Martin has a sheet of 8” by 10” construction paper and cuts the heart
out as shown, what is the area of the heart? Express your answer to the nearest square inch.
The top portion of the heart is made up of two semicircles or the equivalent of one circle. Two diameters stretch the 8 inch
width of the page, so the diameter must be 4 inches and the radius 2 inches. The area of this portion is π × 22 = 4π in2.
The equilateral triangle has a base of 8 inches. Using 30-60-90 triangle ratios, we can find the height to be 4√3 inches.
The area of the equilateral triangle is (1/2) × 8 × 4√3 = 16√3 in2. So, the total area of the heart is 4π + 16√3 ≈ 40 in2.
Problem of the Week Archive
Love is in the Air – February 13, 2017
Problems
Valentine’s day is this week and in the U.S. over 110 million roses will
be sold and delivered between February 13th and February 15th.
Between those dates, the average cost of a dozen florist-arranged,
long-stemmed roses is $73, according to the Society of American
Florists, compared to $59 average for all other dates during the year.
How much more money do florists make selling 110 million roses
over these three days than selling the same amount other days of the
year? Express your answer to the nearest dollar.
What is the percent increase in cost of a rose, based on the information from the previous problem?
Express your answer to the nearest percent.
Martin wants to make a heart shaped card for his valentine.
Martin is in Geometry and loves constructing geometric shapes,
so he decides to make his heart using two semicircles and one
equilateral triangle. The semicircles are tangent to each other and
their diameters lie along one edge of the equilateral triangle. If
Martin has a sheet of 8” by 10” construction paper and cuts the
heart out as shown, what is the area of the heart? Express your
answer to the nearest square inch.