Question

Jude has 5 pairs of sunglasses that cost the same in his online shopping cart, but then decides to get only 2. Each pair of sunglasses is the same price. Let p represent the cost of each pair. Write an expression for the original cost, the updated cost, and the difference in cost.

Answer 1

Let's denote the cost of each pair of sunglasses as p. Since Jude initially had 5 pairs of sunglasses in his online shopping cart, the original cost (OC) can be expressed as the product of the number of pairs (5) and the cost per pair (p):

OC=5p

When Jude decides to purchase only 2 pairs of sunglasses, the updated cost (UC) is the product of the new number of pairs (2) and the cost per pair (p):

UC=2p

To find the difference in cost (ΔC), we subtract the updated cost from the original cost:

ΔC=OC−UC

ΔC=5p−2p

ΔC=3p

So, the expression for the original cost is 5p, the expression for the updated cost is 2p, and the expression for the difference in cost is 3p.

In simpler terms, if the cost of each pair of sunglasses is represented by p, then the original cost is five times the cost of one pair (5p), the updated cost is two times the cost of one pair (2p), and the difference in cost is three times the cost of one pair (3p). This algebraic representation allows us to easily calculate and understand the cost-related changes when Jude decides to purchase fewer pairs of sunglasses.