basic interpretation question about percentages and discounts

Question

Cassandra, during her morning trip to the market, comes across 3 different discounts on mangoes, namely:

[1] Take 3 pay 2 (If you take 6 you pay 4 if you take 4 you pay 3)

[2] 30% off the total purchase price

[3] From the sixth unit (the sixth unit also receives the discount), the next units have a 50% discount

Which of these discounts she should use knowing that her goal is to pay the lowest possible price by taking at least 10 mangoes?

Answer 1

Could assume mangoes $0.10 each.

I. Take 3 pay for 2: 3 would be $0.30, now 3 are $0.20 (pay for 2). Disct is $0.10/0.30 = 33.33..%

Take 6 pay for 4: 6 would be $0.60, now 6 are $0.40 (pay for 4). Disct is $0.20/0.60 = 33.33..%

Take 4 pay for 3: 4 would be $0.40, now 4 are $0.30 (pay for 3). Disct is $0.10/0.40 = 25% (not same as above)

II Compare 30% to above three scenarios.

III Suppose she buys 10 mangoes. 1st 5 @ $0.10 = $0.50; Next 5 @ $0.05 (50% off) = $0.25 Total $0.75

10 would normally by $1.00. Overall disct is $0.25/$1.00 = 25%

Disct gets better with more mangoes. At 20 mangoes, using same logic, overall disct would be 37.5%

Answer 2

We will calculate how much she would pay using all three of these different options.

1) If she takes 9 mangoes, she will pay for 6. She will then take one extra to get to 10. Total payment would be equivalent to 7 mangoes. Further, if she takes 12 mangoes, she would pay for 8. 8/12 is equivalent to 66.6%, so she would receive 33.3% off of her purchase.

2) 30% of 10 is 3, we can calculate this by doing .3*10. If she gets 30% off, she gets the price of three mangoes deducted, so she will pay the equivalent of 7 mangoes. She receives 30% off of her purchase.

3) Mangoes 6,7,8,9, and 10 will be half off. Therefore, 5 of the mangoes will only need to be paid 50% of the price, which would be equivalent to 2.5 mangoes. Add the 5 previous mangoes, and she will pay the equivalent of 7.5 total mangoes. Further, if she takes 11 mangoes, she will pay the equivalent of 8 mangoes. 8/11=72.7%, so she will receive 27.3% off.

Overall, the best option for her would be option 1. Hope this helps!