SOLUTION: A truck loaded with boxes if two different weights. Some of the boxes weigh 6.58kg each and the rest weigh 10.56 kg each. There are 84 more of the heavier boxes than of the lighter

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Question 521076: A truck loaded with boxes if two different weights. Some of the boxes weigh 6.58kg each and the rest weigh 10.56 kg each. There are 84 more of the heavier boxes than of the lighter boxes, and the total weight of all the boxes is 2258.24 kg. How many boxes are there together?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of +6.58+ kg boxes
Let b = number of +10.56+ kg boxes
given:
(1) +6.58a+%2B+10.56b+=+2258.24+
(2) +b+=+a+%2B+84+
------------
substitute (2) into (1)
(1) +6.58a+%2B+10.56%2A%28a+%2B+84%29+=+2258.24+
(1) +6.58a+%2B+10.56a+%2B+887.04+=+2258.24+
(1) +17.14a+=+1371.2+
(1) +a+=+80+
and, since
(2) +b+=+a+%2B+84+
(2) +b+=+80+%2B+84+
(2) +b+=+164+
There are 80 lighter boxes and 164 heavier boxes
check:
(1) +6.58a+%2B+10.56b+=+2258.24+
(1) +6.58%2A80+%2B+10.56%2A164+=+2258.24+
(1) +526.4+%2B+1731.84+=+2258.24+
(1) +2258.24+=+2258.24+
OK