SOLUTION: Sorry, I didn't write the whole problem...A hotel purchased 38 bath towels and 61 washcloths for a total cost of $791.50. A second purchase of 54 bath towels and 50 washcloths, at

Question 1865: Sorry, I didn't write the whole problem...A hotel purchased 38 bath towels and 61 washcloths for a total cost of $791.50. A second purchase of 54 bath towels and 50 washcloths, at the same prices, cost $923. Find the individual prices of the bath towels and washcloths. Hopefully this is more clear and able to be done. Thank you!!!
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
Let t = cost of a towel
let w = cost of a washcloth
38t + 61w = 791.50
54t + 50w = 923
we need to solve these simultaneously. First we need to pick one of te unknowns to get rid of...usually the one that have the same coefficients (the number before it). Here though, both t and w have horrible numbers/coefficients, so we will have to spend sometime messing with these first.
I think it will be easier to get the number of towels the same, rather than washcloths...OK, bite the bullet and multiply the top equation by 54 and the bottom one by 38, giving
2052t + 3294w = 42741
2052t + 1900w = 35074
Now we have the same number of t's...they have the same sign so we Subtract. This gives 1394w = 7667. Hence w = 5.5
Sub this back into either equation...
38t + 61(5.5) = 791.50
38t + 335.50 = 791.50
38t = 456
t=12
cheers
Jon.
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