At a local baseball game, the concession stand has two different meal choices. You can get 3 hotdogs and 1 drinks for $18.00 or you can get 2 hotdogs and 4 drinks for $22.00. If the price of hotdogs and drinks is the same for each meal, find how much it costs for an individual hotdog and an individual drink.

Question

At a local baseball game, the concession stand has two different meal choices. You can get 3 hotdogs and 1 drinks for $18.00 or you can get 2 hotdogs and 4 drinks for $22.00. If the price of hotdogs and drinks is the same for each meal, find how much it costs for an individual hotdog and an individual drink.

Answer 1

To solve this problem, we can set up a system of equations. Let's use the variables H for the cost of an individual hotdog and D for the cost of an individual drink.

From the first scenario, we have:
3H + D = 18 (equation 1)

From the second scenario, we have:
2H + 4D = 22 (equation 2)

We can solve this system of equations using substitution or elimination method. Let's use the elimination method.

Multiply equation 1 by 2 to have an equal number of hotdogs in both equations:
2(3H + D) = 2(18)
6H + 2D = 36 (equation 3)

Now, subtract equation 2 from equation 3:
(6H + 2D) - (2H + 4D) = 36 - 22
6H + 2D - 2H - 4D = 14
4H - 2D = 14 (equation 4)

Now, we have a system of two equations:
4H - 2D = 14 (equation 4)
2H + 4D = 22 (equation 2)

We can solve equation 4 for H and substitute the value in equation 2 to find the value of D.

Multiply equation 4 by 2:
2(4H - 2D) = 2(14)
8H - 4D = 28 (equation 5)

Now, add equation 2 and equation 5:
(8H - 4D) + (2H + 4D) = 28 + 22
8H - 4D + 2H + 4D = 50
10H = 50
H = 50/10
H = $5

Now, substitute the value of H into equation 2:
2($5) + 4D = 22
10 + 4D = 22
4D = 22 - 10
4D = 12
D = 12/4
D = $3

Therefore, an individual hotdog costs $5, and an individual drink costs $3.

Answer 2

To find the cost of an individual hotdog and an individual drink, we need to set up a system of equations using the given information.

Let's assume the cost of a hotdog is represented by 'x' and the cost of a drink is represented by 'y'.

From the first option, we know that 3 hotdogs and 1 drink cost $18.00, so we can write the equation:
3x + y = 18

From the second option, we know that 2 hotdogs and 4 drinks cost $22.00, so we can write the equation:
2x + 4y = 22

Now, we have a system of equations:

Equation 1: 3x + y = 18
Equation 2: 2x + 4y = 22

To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method here:

From Equation 1, we can express y in terms of x:
y = 18 - 3x

Substitute this expression for y in Equation 2:
2x + 4(18 - 3x) = 22

Multiply:
2x + 72 - 12x = 22

Combine like terms:
-10x + 72 = 22

Subtract 72 from both sides:
-10x = -50

Divide by -10:
x = 5

Now that we have found the cost of a hotdog (x = 5), we can substitute it back into Equation 1 to find the cost of a drink:

3(5) + y = 18
15 + y = 18

Subtract 15 from both sides:
y = 3

Therefore, an individual hotdog costs $5.00 and an individual drink costs $3.00.

Answer 3

3h + d = 18

2h + 4d = 22

solve the system by elimination or substitution