Question

Harry and Taylor are running a concession stand for a concert. Hot dogs at the concession stand cost $1.25 each and sodas cost $0.75 each. During one concert, the concession stand earns $352.50 after selling 380 total hot dogs and sodas. The following system of equations can be used to represent the sales at the concession stand where h represents the number of hot dogs sold and s represents the number of sodas sold. 1.25h + 0.75s = 352.50 h + s = 380​ Which ​of the following correctly describes the solution to the system of equations? Group of answer choices

a-135 hot dogs and 245 sodas were sold.
b- 45 hot dogs and 335 sodas were sold.
c- 33 hot dogs and 347 sodas were sold.
d- 125 hot dogs and 255 sodas were sold.

Answer 1

a-135 hot dogs and 245 sodas were sold.

Explanation:

1.25h + 0.75s = 352.50

h + s = 380

h = 380 - s

1.25(380- s) + 0.75s= 352.50

475 - 1.25s + 0.75s = 352.50

122.5 = 0.5s

s = 245

h = 380 - 245

h = 135

Answer 2

a-135 hot dogs and 245 sodas were sold.

Explanation:

Our equations are:

1.25h + 0.75s = 352.50

h + s = 380

Let's use substitution to solve for this system. In the second equation, let's write h in terms of s:

h + s = 380

h = 380 - s

Now, let's plug in 380 - s for h in the first equation:

1.25h + 0.75s = 352.50

1.25(380 - s) + 0.75s = 352.50

We can now solve for s fairly easily:

1.25(380 - s) + 0.75s = 352.50

475 - 1.25s + 0.75s = 352.50

0.5s = 122.5

s = 245 sodas

We can already see which answer choice will match: A, and that is our answer.