Arithmetic reasoning

Question

A family of four have a dinner bill for $44.00. A 15% tip is added after an 8% tax is added to the amount. How much is the tip?

Answer 1

Once the 8% tax is added the total will be $47.52

 

In order to find the tip amount you will then find 15% of $47.52

 

$7.13

Answer 2

 

 

All of it is 100%, 15% = 0.15, and 8%  = 0.08

So 15% increase means multiplying by 100% + 15% = 115% = 1.15 and

8% increase means multiplying by 100% + 8% = 108% = 1.08

 

 

(44 * 1.08 ) * 1.15 = 54.648

 

Note that it doesn't matter whether you tip before or after the tax is added.

To see this, recall that

 

tax then tip =

(44 * 1.08) * 1.15 = 44 * (1.08 * 1.15) <--- associative property

                            = 44 * (1.15 * 1.08) <--- commutative property

                            = (44 * 1.15) * 1.08 <--- associative property again

                            = tip then tax

 

$54.648