PLEASE HELp: You are at Coney Island Amusement Park, and burgers
cost $5 and hot dogs cost $3. You and your friends
spend $45. This is modelled by the equation
5b + 3h= 45.
Is the solution (2, 5) a viable solution?
show your work to the left]

No, the ordered pair (2,5) is not a viable solution

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.

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.

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