Question

At a concession stand, seven hot dog(s) and four hamburger(s) cost $21:25, four hot dog(s) and seven hamburger(s) cost $22.75 Find the cost of one hot dog and the cost of one hamburger

Answer 1

See below ↓↓↓

Explanation:

Given :

• 7 hot dogs + 4 hamburgers = $21.50
• 4 hot dogs + 7 hamburgers = $22.75

Let's set some variables.

• hot dogs = x
• hamburgers = y

So, our equations are :

1. 7x + 4y = 21.50
2. 4x + 7y = 22.75

Mulitply equation #1 by 7 and equation #2 by 4.

• 49x + 28y = 150.50 (Equation 3)
• 16x + 28y = 91.00 (Equation 4)

Subtract equation 4 from equation 3.

• 49x - 16x + 28y - 28y = 150.5 - 91
• 25x = 59.5
• x = $2.38 [cost of one hot dog]

Substitute value of x in equation 4.

• 16(2.38) + 28y = 91
• 38.08 + 28y = 91
• 28y = 52.92
• y = $1.89 [cost of one hamburger]

Answer 2

Explanation:

If 4 hamburger = $21.25

1 hamburger = x

Cross multiply

4 x x = $21.25 x 1

4x = $21.25

Devide both side with the coefficient of x

4x/4 = $21.25/4

X = $5.3125

Therefore 1 hamburger cost $5.31

If 4 hotdogs = $22.75

1 hotdog = y

Cross multiply

4 x y = $22.75 x 1

4y = $22.75

Devide both sides with the coefficient of y

4y/4 = $22.75/4

Y = $5.6875

Therefore one hotdog cost $5.69