SOLUTION: Ken packed some tarts into 16 big and 18 small boxes. There is an equal number of tarts in each big box and an equal number of tarts in each small box. Each big box contained 10 mo

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Ken packed some tarts into 16 big and 18 small boxes. There is an equal number of tarts in each big box and an equal number of tarts in each small box. Each big box contained 10 mo      Log On


   

Question 1193944: Ken packed some tarts into 16 big and 18 small boxes. There is an equal number of tarts in each big box and an equal number of tarts in each small box. Each big box contained 10 more tarts than each small box. 16/25 of the tarts are packed in the big boxes. How many tarts did Ken packed in all?
Found 3 solutions by ikleyn, MathTherapy, greenestamps:
Answer by ikleyn(52775) About Me  (Show Source):
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Ken packed some tarts into 16 big and 18 small boxes.
There is an equal number of tarts in each big box and an equal number of tarts in each small box.
Each big box contained 10 more tarts than each small box.
16/25 of the tarts are packed in the big boxes. How many tarts did Ken packed in all?
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Let x be the number of tarts in each small box; 

then the number of tarts in each big box is (x+10).


The total number of tarts is  16*(x+10) + 18x = 16x + 160 + 18x = 34x + 160.


From the condition, we have this equation

    %2816%2F25%29%2A%2834x%2B160%29 = 16*(x+10).


Simplify and find x

    16*(34x + 160) = 25*16*(x+10)

    544x   +  16*160 = 400x + 4000

    544x - 400x = 4000 - 16*160

       144x     =    1440

          x     =    1440/144 = 10.


ANSWER.  Total tarts = 34x + 160 = 34*10 + 160 = 340 + 160 = 500.

Solved.



Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Ken packed some tarts into 16 big and 18 small boxes. There is an equal number of tarts in each big box and an equal number of tarts in each small box. Each big box contained 10 more tarts than each small box. 16/25 of the tarts are packed in the big boxes. How many tarts did Ken packed in all?
Let equal number in each small box be S
Then equal number in each large box = S + 10
This makes the total in the small boxes 18S, and total in large boxes, 16(S + 10), or 16S + 160
Total number of tarts is then 18S + 16S + 160 = 34S + 160
As 16%2F25 of total number of tarts is in the large boxes, it follows that matrix%281%2C3%2C+1+-+16%2F25%2C+or%2C+9%2F25%29 of the total
number of tarts is in the small boxes. This gives us: matrix%281%2C3%2C+%289%2F25%29%2834S+%2B+160%29%2C+%22=%22%2C+18S%29
                                                          9(34S + 160) = 25(18S) ----- Cross-multiplying 
                                                         306S + 9(160) = 450S
                                                                9(160) = 450S - 306S
                                                                9(160) = 144S
                                          Number in small boxes, or matrix%281%2C7%2C+S%2C%22=%22%2C+9%28160%29%2F144%2C+%22=%22%2C+160%2F16%2C+%22=%22%2C+10%29

Number of tarts packed: 34S + 160 = 34(10) + 160 = 340 + 160 = 500

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of tarts in a small box
Then x+10 is the number of tarts in a large box

He packed 16 big boxes and 18 small boxes:
the number of tarts in the big boxes is 16(x+10)
the number of tarts in the small boxes is 18(x)

16/25 of the tarts were packed in the big boxes, so 9/25 of them were packed in the small boxes. The ratio of the numbers of tarts in the large and small boxes is 16:9.

%2816%28x%2B10%29%29%2F%2818x%29=16%2F9
%28x%2B10%29%2F2x=1
x%2B10=2x
x=10

The number of tarts packed in the large boxes was 16*20 = 320
The number of tarts packed in the small boxes was 18*10 = 180

ANSWER: The total number of tarts was 320+180 = 500