Eight hot dogs and seven hot dog rolls cost $\$13.60$. Seven hot dogs and eight hot dog rolls cost $\$13.40$. How much, in dollars, does a hot dog and a hot dog roll cost combined?

$1.80

Step-by-step explanation:

Let the cost of a hot dog = x

The cost of a hot dog roll = y

Eight hot dogs and seven hot dog rolls cost $\$13.60$.

8x + 7x = $13.60 Equation 1

Seven hot dogs and eight hot dog rolls cost $\$13.40$.

7x + 8x = $13.40 Equation 2

Combining both Equation

8x + 7x = $13.60 Equation 1

7x + 8x = $13.40 Equation 2

Eliminating x

Multiply 1 by 7

Multiply 2 by 8

56x + 49y = 95.2 Equation 3

56x + 64y = 107.2 Equation 4

Subtracting 4 from 3

-15y = -12

y = -12/-15

y = 0.8

Cost of one hot dog roll = $0.8

Solving for x

8x + 7x = $13.60

8x + 7(0.8) = 13.60

8x + 5.6 = 13.60

8x = 13.60 - 5.60

8x = 8.0

x = 8.0/8

x = 1.

Cost of one hot dog = $1.0

The cost in dollars of a hot dog and a hot dog roll cost combined is

x + y

= $1 + $0.8

= $1.80

4x and 6y

im not sure though