Items that are purchased together at a certain discount store are priced at 3USD for the first...

Question

Items that are purchased together at a certain discount store are priced at 3USD for the first item purchased and 1USD for each additional item purchased. What is the maximum number of items that could be purchased together for a total price that is less than 30USD ?

GMAT Panda · Accepted Answer

27 We name n as the number of items purchased together. n = number of items purchased together The total cost is the sum of the cost of the first item and the cost of the remaining items. T = Cost of first item + Cost of remaining items After the first item, each of the remaining n-1 items costs 1 USD, so the total cost is 3 + 1 * (n - 1) T = 3 + 1 (n - 1) We set up the inequality that this total cost is less than 30 USD. 3 + 1 (n - 1) < 30 We simplify the inequality step by step to find the range for the number of items. 3 + 1 (n - 1) < 30 3 + n - 1 < 30 n + 2 < 30 n < 28 Since the number of items must be a positive integer, the greatest integer less than 28 is 27. n = 27

Explanation	Calculations	Help
$We name n as the number of items purchased together.$	$n = number of items purchased together$
$The total cost is the sum of the cost of the first item and the cost of the remaining items.$	$T = Cost of first item + Cost of remaining items$
$After the first item, each of the remaining n-1 items costs 1 USD, so the total cost is 3 + 1 * (n - 1)$	$T = 3 + 1 \times (n - 1)$
$We set up the inequality that this total cost is less than 30 USD.$	$3 + 1 \times (n - 1) < 30$
$We simplify the inequality step by step to find the range for the number of items.$	$3 + 1 \times (n - 1) < 30 3 + n - 1 < 30 n + 2 < 30 n < 28$
$Since the number of items must be a positive integer, the greatest integer less than 28 is 27.$	$n = 27$

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