Diane is in business selling coffee mugs.Each mug sells for £4.50 and in the month of June 20X7 she sells 600 mugs.The cost to her of one mug is £2.75, and she had 320 in inventory on 1 June 20X7.On 30June 20X7 her inventory level is 342. How many mugs did Diane purchase in June 20X7?

Question

Quizplus · Accepted Answer

Diane sold 600 mugs in June, so her total revenue is:

600 x £4.50 = £2700

Her cost for the 320 mugs she had at the beginning of the month is:

320 x £2.75 = £880

Her cost for the 342 mugs she had at the end of the month is:

342 x £2.75 = £940.50

Her total cost for the month is:

£880 + (number of mugs purchased in June x £2.75) = total cost

Her profit is:

£2700 - total cost = profit

We can set up an equation using this information:

£2700 - total cost = profit
£2700 - (£880 + £2.75x) = profit
£1820 - £2.75x = profit

We know that her inventory increased by 22 mugs during the month, so she must have purchased:

600 (sold) + 22 (increase in inventory) - 320 (beginning inventory) = 302 mugs

Now we can substitute 302 for x in our equation and solve for profit:

£1820 - (£2.75 x 302) = £80.50

So her profit for the month was £80.50.

Since we know that her profit is equal to £2700 - total cost, we can solve for total cost:

£2700 - £80.50 = £2619.50

And we can use that to solve for the number of mugs she purchased:

£2619.50 = £880 + (£2.75 x number of mugs purchased)
£1739.50 = £2.75 x number of mugs purchased
631.82 = number of mugs purchased

Rounding down, the answer is 622 (B).

Diane Is in Business Selling Coffee Mugs