Answer: No, the ordered pair (2,5) is not a viable solution
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Explanation:
(2,5) means that b = 2 and h = 5
I'm assuming each ordered pair is of the form (b,h) where b comes first, since b is before h in the alphabet.
So if b = 2 and h = 5, then we can replace each letter with those numbers to get the following:
5b + 3h = 45
5*2 + 3h = 45 ..... b replaced with 2
5*2 + 3*5 = 45 ..... h replaced with 5
10 + 15 = 45
25 = 45
We don't get the same number on both sides, so (b,h) = (2,5) is not a solution.
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Put another way:
If b = 2 and h = 5, this means you bought 2 burgers and 5 hot dogs
1 burger = $5
2 burgers = 2*5 = $10
1 hot dog = $3
5 hot dogs = 5*3 = $15
total amount spent = $10 + $15 = $25
total amount spent = $25
This does not match up with the $45 total spent that we're given. So this is another way to see we don't have a solution.
