Jack intends to purchase a shirt that was originally marked $35 but is now 30% off. Write a linear expression for the new cost of the shirt. Then, calculate the sale price of it.
A) $c-3.5 c, $22.75
B) $c-0.30 c, $24.50
C) $c-0.30 c, $22.75
D) $c-0.35 c, $22.75
Answer (1)
The linear expression for the new cost of the shirt is found by subtracting the discount from the original price: c − 0.30 c .
Calculate the discount amount by multiplying the original price by the discount rate: 0.30 × 35 = 10.50 .
Subtract the discount amount from the original price to find the sale price: 35 − 10.50 = 24.50 .
The sale price of the shirt is $24.50 .
Explanation
Finding the Linear Expression Let c be the original cost of the shirt. The discount is 30% of the original price, which can be written as 0.30 c . The sale price is the original price minus the discount, so the linear expression is c − 0.30 c .
Substituting the Original Price Now, we substitute the original price of the shirt, which is $35 , into the expression to calculate the sale price. So, we have: 35 − 0.30 × 35
Calculating the Discount First, calculate the discount amount: 0.30 × 35 = 10.50
Calculating the Sale Price Next, subtract the discount from the original price to find the sale price: 35 − 10.50 = 24.50 Therefore, the sale price of the shirt is $24.50 .
Final Answer The linear expression for the new cost of the shirt is c − 0.30 c , and the sale price is $24.50 . Therefore, the correct answer is B.
Examples
Understanding discounts is crucial in everyday shopping. For instance, if you want to buy a laptop originally priced at $500 but is 20% off, you can use the expression c − 0.20 c to find the sale price. Substituting c = 500 , you get 500 − 0.20 × 500 = 500 − 100 = $400 . This calculation helps you determine the actual cost and make informed purchasing decisions, ensuring you know exactly how much you're saving.
