Question

This question demonstrates what can happen if you use rounded numerical results too soon. Always keep enough digits in intermediate calculations to arrive at a final answer with sufficient precision.

Consider the following problem.

Suppose you want to buy 100 pens. You can buy 100 pens at a 10% discount at one store where the price is $4.99 per pen. And you can also buy 100 pens at a 15% discount at another store where the price is $5.34 per pen.
(a) What is the price per pen at the first store?
(b) What is the price per pen at the second store?
(c) What is the total price difference for 100 pens?

Answer 1

a) $4.99

b) $5.34

c) $4.8

Explanation:

Hi,

Answers to part a) and b) can be simply picked from the question. For part c), please see the explanation below:

At Store 1:

We bought 100 pen, each for $4.99 ⇒ 100 × 4.99 = $499

At this store, we received a discount of 10%.

10% of 499 ⇒
`(10)/(100)` × 499 = $49.9

We received a discount of $49.9 and hence we paid the final amount of $449.1 at Store 1 for 100 pen.

At Store 2:

We bought 100 pen, each for $5.34 ⇒ 100 × 5.34 = $534

At this store, we received a discount of 15%.

10% of 499 ⇒
`(15)/(100)`× 534 = $80.1

We received a discount of $80.1 and hence we paid the final amount of $453.9 at Store 2 for 100 pen.

Difference:

$453.9 - $449.1 = $4.8

Store 1 is cheaper than Store 2.

Observation:

Had we rounded off both prices in the initial step of the question, then Store 2 would be cheaper than Store 1.

Store 1: $4.99 ≈ $5

Store 2: $5.34 ≈ $5

100 pens at each store would have costed $500.

However, since the discount rate is different and Store 2 offers 15% whereas Store 1 offers only 10% ; Store 2 would have been cheaper than Store 1.