Mary paid $42.50 for 3 diaries and 5 pens yesterday. Today she paid $55 for 4 similar diaries and 6 pens. How much does each item cost separately?

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From the information given we can create two equations. Let the cost of the diaries be D and the cost of the pens be P.

As Mary paid $42.50 for 3 diaries and 5 pens, we have:

3D + 5P = 42.5 ...(1)

And as she paid $55 for 4 similar diaries and 6 pens, we have :

4D + 6P = 55 ...(2)

We have (1) and (2) to solve for D and P.

(2) - (1)

=> D + P = 12.5

=> D = 12.5 - P

Substitute in (1)

3(12.5 - P) + 5P = 42.5

=> 37.5 - 3P + 5P = 42.5

=> 2P = 5

=> P = 2.5

D = 12.5 - 2.5 = 10

**The cost of the diaries is $10 and the pens cost $2.5**

let the cost of pens be x

let the cost of diaries be y

then on the first day,3y+5x=$42.50 (equation 1)

on second day,4y+6x=$55 (equation 2)

on solving 1 and 2 ,we get :y=10;x=2.50

thus,the cost of pens =$2.50

the cost of diaries =$10

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