Solving a fraction problem

Question

Mike is ordering coffee drinks for a monthly staff meeting. 1/4 of the staff ordered a latte, 1/8 of the staff ordered a cappuccino, and 3/5 of the remaining staff ordered an Americano. Some staff members ordered a mocha. If Mike ordered 6 Americanos, how many coffee drinks did he order in total?

Answer 1

1/4 + 1/8 = 2/8+1/8 = 3/8 ordered latte and cappuccino

Then there are 5/8 of the staff remaining, 3/5 of which

ordered Americano. So 3/5 *5/8 = 3/8 ordered Americano

There are X staff members.

3/8 X = 6

X = 6*8/3 = 16 staff members

1/4*16 = 4 latte

1/8*16 = 2 cappuccino

3/8*16 = 6 Americano

which forces 4 mocha