Question

A sporting goods store is having a large sale event. Baseball bats are marked down by 42%, and hockey sticks are marked down by 29%. If baseball bats cost $21. 46 after the markdown and hockey sticks cost $39. 05 after the markdown, which item’s price was reduced by more, and by how many more dollars was it reduced? Round all dollar values to the nearest cent. A. Hockey sticks had their prices reduced by $2. 31 more than baseball bats. B. Hockey sticks had their prices reduced by $0. 41 more than baseball bats. C. Baseball bats had their prices reduced by $4. 22 more than hockey sticks. D. Baseball bats had their prices reduced by $0. 59 more than hockey sticks.

Answer 1

The correct statement is   "Hockey sticks had their prices reduced by $0. 41 more than baseball bats."

Mark down refers to a reduction in price of an item or good. The reduction is generally done as a percentage of price of the item. The purpose behind mark down is to increase sales volume.

Calculation of reduction in price:

Given:

Markdown in price of baseball bats is 42%

Cost of baseball bats after markdown is $21.46

Markdown in price of hockey sticks is 29%

Cost of hockey sticks after markdown is $39.05

For calculating the amount of markdown, we need to find the original cost of baseball bats and hockey sticks.

Calculation of cost of baseball bats before markdown:

$\begin{aligned} \rm Cost \:before\:markdown &= \dfrac{\rm Cost \:after \:Markdown}{100- \rm Markdown\%} \\ \\ &=\dfrac{21.46}{100-42\%}\\ \\ &=\dfrac{21.46}{58\%}\\ \\ &=\ 37\end$

Hence the markdown in price of baseball bats is $\ 37-\ 21.46=\ 15.54$

Similarly, for hockey sticks:

$\begin{aligned} \rm Cost \:before\:markdown &= \dfrac{\rm Cost \:after \:Markdown}{100- \rm Markdown\%} \\\\&=\dfrac{39.05}{100-29\%}\\\\&=\dfrac{39.05}{71\%}\\\\&=\ 55\end$

Markdown in the cost of hockey sticks is $\ 55-\ 39.05=\ 15.95$.

Difference in markdown is:

$\ 15.95-\ 15.54=\ 0.41$

Therefore it can be concluded that markdown in cost of hockey sticks is more as compared to baseball bats by $0.41

Hence the correct statement is "Hockey sticks had their prices reduced by $0. 41 more than baseball bats."

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