Question

you and your friends go to the fair and spend $35 on 10 hot dogs and 5 drinks if the concession stand is advertising seven hot dogs and four drinks for $25.25 what is the cost for one hot dog and one drink.

Answer 1

So for this, you will be doing a system of equations. The first equation will be how much you spent and the second equation is how much they advertise.

Let h = cost of hotdog and d = cost of drinks

`10h+5d=35\\ 7h+4d=25.25`

With this, i'll be using the substitution method. So firstly, subtract 10h on each side of the first equation. It will look like this:
`5d=35-10h`

Next, divide 5 on each side of the first equation. Your answer will be
`d=7-2h`

Next, replace d in the second equation with (7-2h). Your second equation will look like this:
`7h+4(7-2h)=25.25` . From here you can solve for h.

Firstly, foil 4(7-2h).
`7h+28-8h=25.25`

Next, combine like terms:
`28-h=25.25`

Next, subtract 28 on each side to get
`-h=-2.75`

Lastly, multiply -1 on each side of the equation to get
`h=2.75`

Now that we got h, we can solve for d by substituting 2.75 in the h variable in either equation. For this, I'll be using the first one.

`10(2.75)+5d=35\\ 27.5+5d=35\\ 5d=7.5\\ d=1.5`

In short, hotdogs are $2.75 each and drinks are $1.50 each.