A farmer bought a number of pigs for $192. However, 4 of them died before he could sell the rest at a profit of 10 per pig. His total profit was $168. How many pigs did he originally buy?

Answer 1

192=cost of x+4 pigs

4 died leaving x pigs

total profit = $168 for x pigs

with profit per pig =$10

then x = 168/10 = 16.8 pigs and 20.8 original pigs before 4 died

maybe a few pigs died and one on the way out, with only 4/5 of its life left? 1 foot or tail in the grave?

but this ignores the other info, such as $192 cost and 4 pigs dyings

which is irrelevant, useful, but not necessary

so maybe

the additional restriction on a sollution is that x = a whole number, an integer, no fractional pigs allowed

then

try to find an x that gives a whole number both for 192 and 168

try x=20

192/(20+4) = 192/24 = 32/4 = $8 cost per pig

and

168/(20) = $840/100 = $8.40 profit per pig, but it's given that ppp = $10

close but no cigar 8.4 doesn't =10 = the required profit per pig

the more pigs the more total profit, but less profit per pig, so

we need a smaller number of pigs to raise the ppp up a little from 8.4 to 10

that would be 16.8 pigs with 20.8 originally

you could go with 16.8 pigs if its a sort of rolling weighted average,

where it's about 17 pigs for 4 weeks and 16 for 1 week

21 pigs originally 4 weeks and 20 pigs originally for 1 week

averaging out to 20.8 pigs originally and 16.8 after 4 pigs die, on average

another idea

let

x=168

x = 172 = original number of pigs

then

192/172 =about $1.12 cost per pig

168/168 = $1 per pig profit

nope, off by one decimal point tho, close, so close

maybe the original problem was $1680 total profit, and that last zero digit got lost

or another approach

Profit = Revenue minus costs

168 = (price times x) - 192

168+192 = px = 192x/(x+4)

360 = 192x/(x+4)

360(x+4) = 192x

360x+1440 = 192x

360x-192x = -1440

168x = -1440

x = -1440/168 =about -8.57

which makes no sense

x+4 = -4.57= about negative 4.57 pigs

there may be a problem with the defective problem

its parameters seem inconsitent, making a solution the null set

Answer 2

Let x be the number of pigs sold.

Let p be the purchase price per pig.

Purchase:

p(x+4) = 192

p = 192/(x+4)

Sale:

Profit = Revenue - Cost = (p+10)x - 192 = 168

(p+10)x = 360

px + 10x = 360

192x/(x+4) + 10x = 360

192x + 10x(x+4) = 360(x+4)

10x²-128x-1440 = 0

Use the quadratic equation

x = 20, -7.2 Keep the positive value.

Original number:

x+4 = 24 pigs