Coffee, tea, and pastries are sold at a coffe shop. Last week, 2/5 of the coffee shop's profits were from sales and 1/3 of ots profits were from tea sales. The rest of its profits were from pastrie sales. What fraction of the cogfee shop's total profits last week were from pastry sales?

A:1/15

B:2/15

C:4/15

D:11/15

C=coffee T=tea P=pastries

2/5C + 1/3T

2/5=6/15 1/3=5/15

6/15+5/15=11/15

11/15C&T+4/15P=15/15 (total profits)

P=4/15

C: ⁴/₁₅

Step-by-step explanation:

Let

C = fraction of profit from coffee sales

T = fraction of profit from tea sales

P = fraction of profit from pastry sales

C + T + P = 1

Subtract C + T from each side

P = 1 - C - T

= 1 - ⅖ - ⅓

Give all terms the same denominator

Lowest common multiple of 3 and 5 is 15.

P = ¹⁵/₁₅ - ⁶/₁₅ - ⁵/₁₅

Combine the numerators

15 - 6 - 4 = 4

P = ⁴/₁₅

Pastry sales made ⁴/₁₅ of the total profit.