How do you solve this problem?

Question

How do you solve this word problem ?

Mel had some cartons of milk. He sold 2/5 of the cartons in the morning. He then sold 3/4 of the remainder in the afternoon. 24 more cartons were sold in the afternoon than the morning. How many cartons did Melissa start with?

Answer 1

Let x = original number of cartons

 

"sold 2/5 of the cartons in the morning"    means  (2/5)x

 

"sold 3/4 of the remainder in the afternoon"   means  (3/4)(x - (2/5)x)

 

"24 more cartons were sold in the afternoon than the morning"     means

                                         (3/4)(x - (2/5)x)   =     (2/5)x  +  24

 

 (3/4)(x - (2/5)x)   =     (2/5)x  +  24

   15(x - (2/5)x)     =     8x  + 480              [multiply by LCM=20]

    15x - 6x   = 8x + 480                       [distribute[

       x = 480                                     [subtract 8x from both sides]

 

Check:

  Mel sold (2/5)(480)= 192 in the morning, leaving 480-192=288.

  In the afternoon, she sold (3/4)(288)=216.

  The sales in the afternoon were 24 more than in the morning:   216-192=24

Answer 2

Let the number of cartons that Mel had = x

 

Number of cartons sold in morning = 2/5th of what he started = (2/5)*x = 2x/5

 

Remaining cartons = x - 2x/5 = 3x/5

 

Number of cartons sold in afternoon = 3/4th of remainder = (3/4)*(3x/5) = 9x/20

 

24 more cartons were sold in afternoon than morning, which means:

Number of cartons in afternoon = 24 more than morning:

9x/20 = 2x/5 + 24

9x/20 - 2x/5 = 24

x/20 = 24

x = 480

 

Total number of cartons = x = 480

Cartons sold in morning = 2x/5 = 192

Cartons remaining = 480 - 192 = 288

Cartons sold in afternoon = 3/4 of remaining = (3/4) * 288 = 216

 

Afternoon - morning = 216 - 192 = 24