An online buying club offers a membership for $140, for which you will receive a 10 percent discount on all brand-name items you purchase. How much would you have to buy to cover the cost of the membership?
The correct answer and explanation is:
To determine how much you would need to buy to cover the $140 membership cost with a 10% discount, let’s break it down step by step.
Step 1: Understand the problem
The membership costs $140, and with this membership, you receive a 10% discount on all brand-name items. To cover the cost of the membership, the amount you spend on these items must be enough to make up for the $140 membership fee.
Step 2: Set up the equation
Let’s assume the total amount you need to spend on brand-name items is xx. With the 10% discount, you will pay 90% of the original price (because 100% – 10% = 90%). So, the price you actually pay is 0.90×0.90x.
For you to cover the $140 cost of the membership, the amount you spend after the discount must be equal to $140. This gives us the equation: 0.90x=1400.90x = 140
Step 3: Solve the equation
To solve for xx, divide both sides of the equation by 0.90: x=1400.90x = \frac{140}{0.90} x=155.56x = 155.56
Step 4: Interpretation
Therefore, you would need to spend $155.56 on brand-name items to cover the $140 cost of the membership. In other words, if you make purchases worth $155.56, after applying the 10% discount, you will have paid exactly $140, which is the cost of the membership.
Explanation:
This problem is a classic example of a break-even calculation. By offering a discount, the online buying club makes its members pay a smaller percentage of the original price. However, to make the membership worth it, the total amount of money spent (before the discount) must be higher than the membership fee. By spending $155.56, the discount reduces the price enough to make it equal to the $140 membership, meaning you effectively cover the cost of joining the club.