WAEC 2017 · Paper 2 · Q5

Out of 120 customers in a shop, 45 bought bags and shoes. All the customers bought either bags or shoes, and 11 more customers bought shoes than bags.

(a)
Illustrate this information in a diagram.
Model answer
Two overlapping circles, $B$ (bags) and $S$ (shoes), in a rectangle for all 120 customers: 45 in the overlap, $x$ in bags only and $x + 11$ in shoes only, and 0 outside (everyone bought one or the other). Then $x + 45 + x + 11 = 120$ gives $x = 32$ , so the regions are 32, 45 and 43.
(b)
Find the number of customers who bought shoes.
(c)
Calculate the probability that a customer selected at random bought bags.

Worked solution (try it first)

(a)

Draw two overlapping circles, B (bags) and S (shoes), inside a rectangle of 120 customers.
Put 45 in the overlap.
Let $x$ customers buy bags only.
Then "11 more bought shoes than bags" makes shoes only $x + 11$ .
Nobody is outside both circles.
Everyone is in the diagram, so $x + 45 + (x + 11) = 120$ .
That gives $2x + 56 = 120$ , $2x = 64$ and $x = 32$ .

(b)

Shoes: $45 + (32 + 11) = 88$ customers.

(c)

Bags: $32 + 45 = 77$ customers, so $P(\text{bought bags}) = \frac{77}{120}$
$\approx 0.642$ .

Report a problem with this question