Jack intends to purchase a shirt that was originally marked $[tex]$35$[/tex] but is now [tex]$30 \%$[/tex] off. Write a linear expression for the new cost of the shirt. Then, calculate the sale price of it.
A) $[tex]$c-0.30 c, $24.50$[/tex]
B) $[tex]$c-0.35 c, $22.75$[/tex]
C) $[tex]$c-0.30 c, $22.75$[/tex]
D) $[tex]$c-3.5 c, $22.75$[/tex]
Answer (2)
Define the original cost as c , and the discount as 0.30 c .
Express the sale price as the original cost minus the discount: c − 0.30 c .
Substitute the original price of $35 into the expression: $35 − 0.30 ( \3 5 ) .
Calculate the sale price: $35 − $10.50 = $24.50 .
Explanation
Problem Analysis Let's analyze the problem. We are given the original price of a shirt and the discount percentage. We need to find a linear expression representing the sale price and then calculate the actual sale price.
Formulating the Expression Let c be the original cost of the shirt, which is $35 . The discount is 30% of the original price, which can be expressed as 0.30 c . The sale price is the original price minus the discount, which can be expressed as c − 0.30 c .
Calculating the Sale Price Now, let's substitute c = $35 into the expression c − 0.30 c to calculate the sale price: $35 − 0.30 ( \3 5 ) $35 − $10.50 = $24.50
Final Answer Therefore, the linear expression for the new cost of the shirt is c − 0.30 c , and the sale price is $24.50 .
Examples
Imagine you're at a store where everything is 20% off. This problem helps you calculate the final price of an item quickly. For instance, if a video game originally costs $50 , you can use the expression c − 0.20 c to find the sale price. Substituting c = $50 , you get $50 − 0.20 ( \5 0 ) = $50 − $10 = $40 . This method is useful for budgeting and making informed purchasing decisions in everyday shopping scenarios.
The linear expression for the new cost of the shirt is c − 0.30 c , which simplifies to 0.70 c . The calculated sale price of the shirt is $24.50. The correct choice is A) c − 0.30 c , $24.50 .
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