Question

Patrick bought some dictionaries and files for $1 474.
The number of dictionaries he bought was 2/3 the number of files he bought.
The cost of a dictionary was $12 more than the cost of a file.
He spent $22 more on dictionaries than on files.
How much did a dictionary cost?

Answer 1

d = 2/3 f
If dictionaries cost x and files cost y, then
x = y+12
d*x = f*y + 22
d*x + f*y = 1474
Now solve for x

Answer 2

Number of files f
number of dictionaries = 2f/3
cost of a file: x
cost of dictionary : x+12

(2f/3)(x+12) - fx = 22
times 3
2f(x+12) - 3fx = 66
2fx + 24f - 3fx = 66
24f - fx = 66 or
f = 66/(24-x)


we also know that fx + (2f/3)(x+12) = 1474
3fx + 2f(x+12) = 4422
5fx + 24f = 4422
f = 4422/(5x + 24)

66/(24-x) = 4422/(5x + 24)
330x + 1584 = 106128 - 4422x
4752x = 104544
x = 22

f = 66/(24-22) = 33

I defined the cost of a dictionary as x+12
So a dictionary costs 34

check:
cost of dictionary --- 34
cost of file ---- 34
number of files --- 33
number of dict's --- 22
total cost = 33(22) + 22(34) = 1474
looks good to me

Note, this is obviously not the only way.