Question

Mr. Javier purchased a number of pencils for ₱180 and sold all except 6 at a profit of ₱2 per pencil. With the total amount received, he could buy 30 more items than before. Find the number of items he bought and the cost of each in pesos

Answer 1

Answer:

36 pencils

$Cost = 0.2$

Step-by-step explanation:

Given

Cost Price = 180

Represent the number of items by x

This implies that the cost of each item is $\frac{x}{180}$

$Selling\ Price = Cost + Profit$

$Selling\ Price = \frac{x}{180} + 2$

Since all but 6 items were sold, the total selling price is:

$Total = (x - 6)(\frac{x}{180} + 2)$

This amount can be used to buy 30 more items.

So, we have:

$(x - 6)(\frac{x}{180} + 2) = x + 30$

Multiply both sides by 180

$180 * (x - 6)(\frac{x}{180} + 2) =180(x + 30)$

$(x - 6)(x + 360) = 180x + 5400$

Expand brackets

$x\² + 360x - 6x - 2160 = 180x + 5400$

$x\² + 354x - 2160 = 180x + 5400$

Equate to 0

$x\² + 354x - 180x - 2160 - 5400 = 0$

$x\² + 174x - 7560 = 0$

Expand

$x\² + 210x - 36x - 7560 = 0$

$x(x + 210) - 36(x + 210) = 0$

$(x - 36)(x + 210) = 0$

$x - 36 = 0$ or $x + 210 = 0$

$x = 36$ or $x = -210$

Since, number of items can't be negative, we have to discard x = -210.

Hence:

$x = 36$

We can then conclude that, Mr. Javier purchased 36 pencils

Recall that

$Cost = \frac{x}{180}$

$Cost = \frac{36}{180}$

$Cost = 0.2$