Paintings are sold in an art gallery - OCR - GCSE Maths - Question 10 - 2020 - Paper 6

Let the original cost of the painting be represented as $C$. Adding k% commission gives:

C_{total} = C + rac{k}{100}C = C(1 + rac{k}{100})

Next, we apply a 15% tax on this total cost:

$Price o pay = C_{total} + 0.15 imes C_{total} = C_{total}(1 + 0.15) = C_{total} imes 1.15$

According to Layla, the price to pay is:

$Price o pay = C imes 1.403$

Equating the two expressions we derived gives:

C(1 + rac{k}{100}) imes 1.15 = C imes 1.403

Dividing both sides by C (assuming C ≠ 0):

(1 + rac{k}{100}) imes 1.15 = 1.403

Now we can isolate the term:

1 + rac{k}{100} = rac{1.403}{1.15}

Calculating the right-hand side:

1 + rac{k}{100} ext{ approximately equals } 1.22

Thus:

rac{k}{100} = 1.22 - 1 = 0.22

And multiplying by 100 to find k:

$k = 22$