Answer: between $42 and $54 including both endpoints.
In symbolic form we can say
where p is the final price after the discount is applied.
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Explanation:
10% off means you save 10% but pay the remaining 90%
Then convert 90% to decimal form to get 0.90
If the original price is $60, then the final price is 0.90*60 = 54 dollars.
In other words,
10% of 60 = 0.10*60 = 6 dollars saved
60-6 = 54 is the final price
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If the discount is 30% then you pay the remaining 70%
0.70*60 = 42
Or you can think of it like this
30% of 60 = 0.30*60 = 18 dollars saved
60-18 = 42 dollars is the final price
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Let's summarize with this chart:
![\begin{array}{|c|c|c|} \cline{1-3}\text{Discount} & \text{Amount Saved} & \text{Final Price}\\\cline{1-3}10\% & \$6 & \$54\\\cline{1-3}30\% & \$18 & \$42\\\cline{1-3}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7Cc%7C%7D%20%5Ccline%7B1-3%7D%5Ctext%7BDiscount%7D%20%26%20%5Ctext%7BAmount%20Saved%7D%20%26%20%5Ctext%7BFinal%20Price%7D%5C%5C%5Ccline%7B1-3%7D10%5C%25%20%26%20%5C%246%20%26%20%5C%2454%5C%5C%5Ccline%7B1-3%7D30%5C%25%20%26%20%5C%2418%20%26%20%5C%2442%5C%5C%5Ccline%7B1-3%7D%5Cend%7Barray%7D)
Therefore, the final price after the discount is between $42 and $54 including both endpoints.
Side note: The jump from 10% to 30% is "times 3"; so is the jump from $6 to $18 in the "amount saved" column of the table.