Claire is shopping at a shoe store. The store is having a sale and discounting all shoes by 35% of the marked price. She decides to buy a pair of shoes with a marked price of $64.99 Set up a proportion that can be used to find the dollar amount of the discount (d).
Let d be the dollar amount of the discount.
If the discount is 35% of the marked price, then the dollar amount of the discount can be calculated as follows:
35% * $64.99 = (35/100) * $64.99 = $<<35/100*64.99=22.75>>22.75
The dollar amount of the discount can be represented by the proportion:
d/1 = $22.75/$64.99
Given that the sales tax in Claire's state is 7.5%, what is the final cost of the shoes Claire buys from the shoe store?
Let p be the final cost of the shoes without including sales tax.
The final cost of the shoes with sales tax can be calculated as follows:
p + 7.5% * p = (1 + 7.5/100) * p = (1.075) * p
Since the dollar amount of the discount is $22.75, the final cost of the shoes after the discount can be calculated as follows:
p = $64.99 - $22.75 = $42.24
Substituting this value into the equation above, we can find the final cost of the shoes with sales tax:
(1.075) * $42.24 = $45.37
Therefore, the final cost of the shoes Claire buys from the shoe store is $45.37.
Claire's cousin, Sara, lives in a different state with a 5% sales tax rate. Sara found the same pair of shoes discounted 40% from a regular price of $67.00.
If Sara bought the shoes, who paid the lower total cost? Justify your answer.
To compare the total cost paid by Claire and Sara, we need to calculate the final cost of the shoes for both of them.
For Claire:
The marked price of the shoes is $64.99.
The discount is 35% of the marked price, which is $22.75.
Therefore, the final cost of the shoes for Claire, including sales tax, is $45.37.
For Sara:
The marked price of the shoes is $67.00.
The discount is 40% of the marked price, which is $26.80.
Therefore, the final cost of the shoes for Sara, without including sales tax, is $67.00 - $26.80 = $40.20.
Now let's calculate the final cost of the shoes for Sara, including sales tax.
The sales tax rate in Sara's state is 5%.
Therefore, the sales tax on the final cost of the shoes would be 5% of $40.20, which is $2.01.
Therefore, the final cost of the shoes for Sara, including sales tax, is $40.20 + $2.01 = $42.21.
Comparing the final costs:
- Claire paid $45.37.
- Sara paid $42.21.
Therefore, Sara paid the lower total cost for the shoes.
Sonya included the heights of two more 6th grade boys to create a new data set. One is shorter than all the other boys in 6th grade, and one is taller than all the other boys in 6th grade.
Which measure(s) must be the same when the two boys' heights are included? Justify your answer.
When the heights of the two additional boys are included in the data set, the only measure that remains the same is the Maximum height. This is because adding a shorter boy will not affect the minimum height, and adding a taller boy will only change the maximum height if they are taller than the previous tallest boy.
Other measures such as the Mean, Median, and Range will all be affected by the inclusion of these new heights. The mean will change as the sum of all the heights will now include the heights of the two new boys. The median will change if the new boys' heights fall in the middle of the ordered data set. Finally, the range will change as the difference between the minimum and maximum height will depend on the heights of the two additional boys.