Question

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

Answer 1

Answer:

$6.00

Step-by-step explanation:

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:

$2h + 3w = 18$

We can rearrange the equation to make w the subject:

⇒ $3w = 18 - 2h$

⇒ $w = \frac{18 - 2h}{3}$

• For the second family:

$4h + 2w = 28$

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:

⇒ $4h + 2(\frac{18 - 2h}{3}) = 28$

⇒ $4h + \frac{36 - 4h}{3} = 28$

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

⇒ $8h + 36 = 84$

⇒ $8h = 48$

⇒ $h = \bf 6$

∴ The price of one hot dog is $6.00.