Question

A shipment of 205 Otter Box covers for i-phones has just arrived. The total invoice (excluding tax, shipping, etc.) is $ 4,829.75 The Otter Box "Defender" cover is priced at $39.95 The Otter Box "Case" cover is priced at $18.95 How many Otter Box "Defender" series covers are in the shipment?

Answer 1

45 otter box defender series covers are in the shipment

Solution:

Let the number of Otter Box Defender cover be x

Let the number of Otter Box Case cover be y

Cost of 1 Otter Box Defender cover = $ 39.95

Cost of 1 Otter Box Case cover = $ 18.95

Given that shipment of 205 Otter Box covers for i-phones has just arrived

Therefore,

number of Otter Box Defender cover + number of Otter Box Case cover = 205

x + y = 205 ---------- eqn 1

Given that total invoice is $ 4829.75

Therefore,

number of Otter Box Defender cover x Cost of 1 Otter Box Defender cover + number of Otter Box Case cover x Cost of 1 Otter Box Case cover = 4829.75

$x \times 39.95 + y \times 18.95 = 4829.75$

39.95x + 18.95y = 4829.75 ------ eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 205 - y ----- eqn 3

Substitute eqn 3 in eqn 2

39.95(205 - y) + 18.95y = 4829.75

8189.75 - 39.95y + 18.95y = 4829.75

-21y = 4829.75 - 8189.75

-21y = -3360

y = 160

From eqn 3,

x = 205 - y

x = 205 - 160

x = 45

Thus 45 otter box defender series covers are in the shipment