At the end of 2019, a company reported cost of goods sold of $4,800, which represented 80% of the goods available for sale. The beginning inventory amount was twice as much as the ending inventory amount. What was the amount of purchases for 2019?

Question

Quizplus · Accepted Answer

Let's start with the formula for cost of goods sold (COGS):
COGS = Beginning inventory + Purchases - Ending inventory

We know that COGS for 2019 was $4,800 and that ending inventory was half of beginning inventory. Let's use an algebraic equation for beginning inventory (BI):
BI = 2 x EI

Now let's plug in the values we know into the COGS formula:
$4,800 = BI + Purchases - $2,400

We can simplify this to:
$4,800 = 2 x EI + Purchases

And we know that purchases plus ending inventory equals the goods available for sale:
Purchases + EI = GAS

Since we know that COGS was 80% of GAS, we can write another equation:
COGS = 80% x GAS
$4,800 = 0.8(GAS)

Now we can plug in our known values for GAS and solve for Purchases:
GAS = Purchases + EI
GAS = Purchases + $2,400 (since EI was given as half of beginning inventory)
$4,800 = 0.8(Purchases + $2,400)
$4,800 = 0.8Purchases + $1,920
$2,880 = 0.8Purchases
Purchases = $3,600

Therefore, the amount of purchases for 2019 was $3,600. Choice C is the correct answer.

At the End of 2019, a Company Reported Cost of Goods