Question

Mike bought five items for lunch that Cost a total of 4.55 .Hit dogs cost .1.10 each and cookies cost 0.75 each. What equation could be used to find h the number of hot dogs and c the number of cookies

Answer 1

`c + h = 5` and

`0.75c + 1.10h = 4.55`

Explanation:

Assume that Mike bought only cookies and hot dogs.

The total can be represented as:

`Cookies + Hot\ Dogs = 5` --- (1)

And the amount spent can be represented as:

`Cost\ of\ cookies + Cost\ of\ hot\ dogs = 4.55` --- (2)

Required

Determine the system of equation

Let c represents the number of cookies and h, number of hot dogs.

`Cookies + Hot\ Dogs = 5` implies
`c + h = 5`

And

`Cost\ of\ cookies + Cost\ of\ hot\ dogs = 4.55`

Cost of cookies = 0.75 * c

Cost of hot dogs = 1.10 * h

So, we have:

`0.75c + 1.10h = 4.55`

Hence, the equations are:

`c + h = 5` and

`0.75c + 1.10h = 4.55`

Solving for c and h

Make c the subject in
`c + h = 5`

`c = 5 - h`

Substitute 5 - h for c in
`0.75c + 1.10h = 4.55`

`0.75(5- h) + 1.10h = 4.55`

`3.75- 0.75h + 1.10h = 4.55`

`3.75 +0.35h = 4.55`

Collect Like Terms

`0.35h = 4.55 - 3.75`

`0.35h = 0.8`

Solve for h

`h = 0.8/0.35`

`h = 2.28571428571`

`h =2` -- approximated

Recall that:

`c = 5 - h`

`c = 5 - 2`

`c =3`