Be a wise consumer!

Algebra Level 2

Isarence loves Happy Brand Chocolate Chip Cookies! Recently, she won a competition held by The Happy Food Company, and got a voucher for Happy Brand Chocolate Chip Cookies. Hooray! Here are the terms of the voucher:

  1. This voucher is valid for a purchase of 10 boxes of Happy Brand Chocolate Chip Cookies in a single receipt.
  2. This voucher provides a 20% discount from the displayed price of the cookies (discount is applied to all 10 boxes)
  3. This voucher is valid for use at the following supermarkets: Applemart, Bestprice and Cheapstuff.

One weekend, Isarence went to the supermarket district in town to use her voucher. All 3 participating outlets had a store there, how convenient! It is known that the market price of a box of Happy Brand Chocolate Chip Cookies was $10 on that day. She went to all 3 stores to check out their prices.

The displayed price for the cookies at Applemart was the same as the market price of the cookies. However, Isarence has an Applemart Members Card, which entitles her to an additional 15% discount on all items in the store, based on their displayed prices.

Bestprice was having a sale that day, and the displayed prices for all items were 20% less than the market prices.

Cheapstuff always had cheaper prices, and it was found that the displayed price of the cookies was 5% lower than the market price. On top of that, for every 10 boxes purchased, she will receive a discount of $10, given after all the other discounts are calculated. How wonderful!

Now, Isarence loves cookies, but she isn't very accurate in counting, so she needs your help! Which store has the lowest price for 10 boxes of Happy Brand Chocolate Chip Cookies?

Applemart and Bestprice Cheapstuff Applemart Applemart and Cheapstuff Bestprice and Cheapstuff Bestprice All of them end up with the same amount Cannot be determined

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2 solutions

Hung Woei Neoh
Jul 5, 2016

The displayed price of a box of cookies at Applemart is $ 10 \$10 . There, she gets a discount of 15 % + 20 % = 35 % 15\%+20\% = 35\% on each box of cookies.

Therefore, the cost of buying at Applemart = 10 × ( 100 35 ) % × 10 = 100 × 65 100 = $ 65 =10 \times (100-35)\% \times 10 = 100 \times \dfrac{65}{100} = \$65

At Bestprice, the displayed price was lower than the market price by 20 % 20\% .

Therefore, the cost of buying at Bestprice = 10 × ( 100 20 ) % × ( 100 20 ) % × 10 = 100 × 80 100 × 80 100 = 6400 100 = $ 64 =10 \times (100-20)\% \times (100-20)\% \times 10 = 100 \times \dfrac{80}{100} \times \dfrac{80}{100} = \dfrac{6400}{100} = \$64

At Cheapstuff, the displayed price was lower than 5 % 5\% , and after calculating the discount, there is an additional $ 10 \$10 discount.

Therefore, the cost of buying at Cheapstuff = 10 × ( 100 5 ) % × ( 100 20 ) % × 10 10 = 100 × 95 100 × 80 100 10 = 7600 100 10 = 76 10 = $ 66 =10 \times (100-5)\% \times (100-20)\% \times 10 - 10 = 100 \times \dfrac{95}{100} \times \dfrac{80}{100} - 10 = \dfrac{7600}{100}-10 = 76-10 = \$66

From here, we can see that Bestprice \boxed{\text{Bestprice}} has the lowest price for 10 10 boxes of Happy Brand Chocolate Chip Cookies

Jrp Gamez
Jul 8, 2016

Percentages are constant so I just did all get 20% discount so forget that part 1 gives straight up 15% off the other 20% off and 1 gives 5% and $10 so $10 of $100 total price is 10% so that is 15% total so the answer is the 20% discount... maybe I just got lucky but that's how my simple brain works.

According to your solution option 1 and 3 are equal which is not true so I think you got lucky :)

Alexander Kies - 4 years, 10 months ago

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