SOLUTION: clair bought two bars of soap and six sponges for $5.50. steve bought three bars of soap and five sponges for $8.25. what is the cost for each item?

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Question 617635: clair bought two bars of soap and six sponges for $5.50. steve bought three bars of soap and five sponges for $8.25. what is the cost for each item?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the cost of a bar of soap
Let +b+ = the cost of a sponge
given:
(1) +2a+%2B+6b+=+5.5+
(2) +3a+%2B+5b+=+8.25+
-------------------
Multiply both sides of (1) by 3
Multiply both sides of (2) by 2
Then subtract (2) from (1)
(1) +6a+%2B+18b+=+16.5+
(2) +-6a+-+10b+=+-16.5+
+8b+=+0+
+b+=+0+
and
(1) +2a+=+5.5+
(1) +a+=+2.75+
and
(2) +3a+=+8.25+
(2) +a+=+2.75+
It looks like the bars of soap are $2.75 each
and the sponges are free.