Two families visited an amusement park. The first family bought 2 hot dogs and 3 bottles of waters, which totaled $18. The second family bought 4 hot dogs and 2 bottles of waters, which totaled $28. How much did one hot dog cost?

$2
$4
$5
$6
The answer is 6.
6x4=24
and that leaves the water to =2 per bottle.
so, 24+4=28

To solve this problem, we have to construct two separate equations for each family, and then use any of the methods for solving simultaneous equations.

Let's consider h to represent the cost of 1 hot dog, and w to mean the cost of 1 water bottle.

• For the first family:

[tex]2h + 3w = 18[/tex]

We can rearrange the equation to make w the subject:

⇒ [tex]3w = 18 - 2h[/tex]

⇒ [tex]w = \frac{18 - 2h}{3}[/tex]

• For the second family:

[tex]4h + 2w = 28[/tex]

Since we have previously obtained an expression for w in terms of h, we can substitute that expression for w in the above equation, and then solve for h:

⇒ [tex]4h + 2(\frac{18 - 2h}{3}) = 28[/tex]

⇒ [tex]4h + \frac{36 - 4h}{3} = 28[/tex]

⇒ [tex]12h + 36 - 4h = 84[/tex] [Multiplying both sides of the equation by 3]

⇒ [tex]8h + 36 = 84[/tex]

⇒ [tex]8h = 48[/tex]

⇒ [tex]h = \bf 6[/tex]

∴ The price of one hot dog is $6.00.