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Chapter 16: Problem 13

A \(30 \%\) discount reduces the price of a commodity by $$\$ 90$$. If the discount is reduced to \(20 \%\), then the price of the commodity will be (A) $$\$ 180$$ (B) $$\$ 210$$ (C) $$\$ 240$$ (D) $$\$ 270$$ (E) $$\$ 300$$

Short Answer

Expert verified
The price will be $240, choice (C).

Step by step solution

01

Understand the relationship between discount and original price

Given a 30% discount reduces the price of a commodity by $90. This means 30% of the original price equals $90. Let's find the original price using the relationship that 0.3 times the original price equals $90.
02

Calculate the original price

Let \( x \) be the original price. From Step 1, we have \( 0.3x = 90 \). Solving for \( x \), we divide both sides by 0.3:\[ x = \frac{90}{0.3} = 300 \]
03

Calculate the new price with a 20% discount

The problem states that the discount is reduced to 20%. Hence, the discounted amount is now 20% of the original price. Calculate 20% of the original price:\[ 0.2 \times 300 = 60 \]
04

Calculate the selling price with the new discount

Subtract the 20% discount from the original price to find the new selling price:\[ 300 - 60 = 240 \]
05

Identify the correct answer from the options

From Step 4, we found the new selling price is $240. Therefore, the correct answer is (C) $240.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percentage Discount
In math, understanding percentage discounts is vital for problems involving price reductions. A percentage discount is the reduction in price expressed as a percentage of the original price. It helps quantify how much cheaper an item is compared to its original selling price.

Here's how it works: if you have a 30% discount on an item, it means you're paying 70% of the original price. The 30% signifies the amount deducted.
  • 30% discount means you pay 70% of the original price.
  • 20% discount means you pay 80% of the original price.
In our example, a 30% discount reduced the price by $90. It implies that 30% of the original price translates to $90.
Original Price Calculation
Finding the original price is crucial in solving discount-related math problems. Once you know the discount and the amount it translates to, you can determine the original price.

To calculate the original price from a percentage discount, first express the discount amount as an equation. In our example, 30% of the original price equals \(90, or mathematically stated, as: \( 0.3 \times \text{original price} = 90 \).

To isolate the original price variable, divide both sides by the discount percentage in decimal form:
  • \( \frac{90}{0.3} = 300 \)
This calculation shows the original price before the discount was applied was \)300.
Step-by-Step Solution
When tackling math problems, a step-by-step solution is like your guiding map, ensuring you don't get lost.

Start by understanding the relationship between discount and price. Identify given data and relationships. Here, a 30% discount equals \(90.
  • Step 1: Establish the equation: \( 0.3x = 90 \).
  • Step 2: Solve for \( x \) by dividing both sides by 0.3, resulting in an original price of \)300.
  • Step 3: With the new 20% discount, calculate how much will be deducted from \(300: \( 0.2 \times 300 = 60 \).
  • Step 4: Subtract the \)60 discount from \(300.
  • Step 5: Verify and choose the correct answer from given options: \)240.
Following steps systematically reduces errors and improves understanding.
Solving Equations
Solving equations is a fundamental skill in math that applies to numerous problems, including those with discounts. It involves finding the value of a variable that satisfies the equation.

In discount problems, equations often illustrate the relationship between the discount percentage and the original price. For instance, the equation \( 0.3x = 90 \) was essential to finding the original price. By solving it, you isolate \( x \).

To solve, perform simple arithmetic operations to both sides of the equation:
  • Divide both sides by 0.3: \( x = \frac{90}{0.3} \).
Understanding how to manipulate equations correctly is crucial. It ensures you find accurate solutions in price discount problems and beyond.

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Most popular questions from this chapter

Last month the price of a particular pen was $$\$ 1.20$$. This month the price of the same pen is $$\$ 1.50$$. What is the percent increase in the price of the pen? (A) \(5 \%\) (B) \(10 \%\) (C) \(25 \%\) (D) \(30 \%\) (E) \(33 \frac{1}{3} \%\)

John bought a shirt, a pair of pants, and a pair of shoes, which cost $$\$ 10, \$ 20$$, and $$\$ 30$$, respectively. What percent of the total expense was spent for the pants? (A) \(16 \frac{2}{3} \%\) (B) \(20 \%\) (C) \(30 \%\) (D) \(33 \frac{1}{3} \%\) (E) \(60 \%\)

If \(15 \%\) of a number is \(4.5\), then \(45 \%\) of the same number is (A) \(1.5\) (B) \(3.5\) (C) \(13.5\) (D) 15 (E) 45

John spent $$\$ 25$$, which is 15 percent of his monthly wage. What is his monthly wage? (A) $$\$ 80$$ (B) $$\$ 166 \frac{2}{3}$$ (C) $$\$ 225$$ (D) $$\$ 312.5$$ (E) $$\$ 375$$

A jar contains 24 blue balls and 40 red balls. Which one of the following is \(50 \%\) of the blue balls? (A) 10 (B) 11 (C) 12 (D) 13 (E) 14
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