Been trying for too long.

Question

Mrs Chen made some tarts. She sold 3/5 of them in the morning and 1/4 of the remainder in the afternoon.

 

If she sold 200 more tarts in the morning than in the afternoon, how many tarts did she make?

Answer 1

3/5 in the morning. That leaves 2/5. 1/4 of that 2/5 were sold in the afternoon.

That is 1/10.

 

3x/5 = x/10 + 200

6x/10 - x/10 = 200

5x/10 = 200

x/2 = 200

x = 400

Answer 2

Let x be the total number of tarts.

 

   Morning sales = (3/5)x

   Afternoon sales = (1/4)( x - (3/5)x )        ["1/4 of the remainder"]

 

   Morning sales = afternoon sales  + 200        ["200 more ... in the morning than in the afternoon"]

 

What is x?

 

      (3/5)x  =  (1/4)( x - (3/5)x )  +  200

       (3/5)x = (1/4)x - (1/4)(3/5)x + 200

        3x  =  (5/4)x - (1/4)(3)x + 1000        [multiply by 5]

        12x = 5x - 3x + 4000               [multiply by 4]

         10x = 4000

          x = 400

 

Check:

    Morning sales = (3/5)(400) = 240

    Afternoon sales = (1/4)(160) = 40

   Yes, 240 is 200 more than 40.