Problem of the Week Archive
Cyber Monday – November 30, 2015
Problems & Solutions
Cyber Monday is the Monday after Thanksgiving. Many online retailers
offer discounts and promotions and it is considered to be the biggest
online shopping day of the year. Cyber Monday sales have increased
every year since 2005. The table shows the sales, in millions of
dollars, for the years 2005 to 2014. Between which two years was
the smallest percent increase in sales seen? What was the percent
increase? Express your answer to the nearest whole number.
The smallest total increase in overall sales was between 2008 and 2009. The sales
difference was 887 – 846 = 41 million dollars. This is a percent increase of
41 ÷ 846 × 100 ≈ 5%.
Year
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
Sales (millions)
$484
$610
$730
$846
$887
$1028
$1251
$1465
$1735
$2038
It is estimated that on Cyber Monday in 2014, shoppers spent an average of $125 per order. If this
estimate is correct, how many orders were placed?
From the table we can see that in 2014 the total sales was $2038 million. If the average amont per order was $125 then
there were $2,038,000,000 ÷ $125/order = 16,304,000 orders.
This year for Cyber Monday, analysts are expecting sales, once again, to increase from the previous
year, but they believe there will be a decrease in the number of orders placed. In 2015 if sales
increase 13% and the number of orders decreases 4%, compared to 2014, based on the previous
problems, how much more will be spent, on average, per order in 2015? Express your answer to the
nearest whole number.
If sales increase 13%, the total sales will be 100 + 13 = 113% of the previous year’s total sales. Sales will increase from
$2038 million in 2014 to 1.13 × $2038 million = $2302.94 million in 2015. If the number of orders decreases 4%, the
number of orders will be 100 – 4 = 96% of the previous year’s orders. The number of orders will decrease from
16,304,000 orders in 2014 to 0.96 × 16,304,000 = 15,651,840 orders in 2015. The average amount spent per order
will be $2,302,940,000 ÷ 15,651,840 = $147 per order. The amount spent per order will increase $147 – $125 = $22.