Question

Jackie purchased 3 bottles of water and 2 cups of coffee for a family for $7.35. Brian bought 4 bottles of water and 1 cup of coffee for his family for $7.15. how much does each bottle of water cost? how much does each cup of coffee cost? Please I need this done

Answer 1

Cost of each cup of coffee is $1.59.

Cost of each bottle of water is $1.39.

Explanation:

Let C be the cost of each cup of coffee and B be the cost of each bottle of water.

We have been given that Jackie purchased 3 bottles of water and 2 cups of coffee for the family. So the cost of 3 bottles of water will be 3B and cost of 2 cups of coffee will be 2C.

As Jackie spent $7.35 on these items, so we can represent this information in an equation as:

`3B+2C=7.35...(1)`

We are also told that Ryan bought 4 bottles of water and 1 cup of coffee for his family. So the cost of 4 bottles of water will be 4B and cost of 1 cup of coffee will be C.

As Ryan spent $7.15 on these items, so we can represent this information in an equation as:

`4B+C=7.15...(2)`

To find the cost of one cup of coffee we will solve our system of equations using substitution method.

From equation (2) we will get,

`C=7.15-4B`

Substituting this value in equation (1) we will get,

`3B+2(7.15-4B)=7.35`

Upon using distributive property we will get,

`3B+14.30-8B=7.35`

Let us combine like terms.

`3B-8B+14.30-14.30=7.35-14.30`

`-5B=-6.95`

Upon multiplying both sides of our equation by -5 we will get,

`(-5B)/(-5)=(-6.95)/(-5)`

`B=1.39`

Therefore, the cost of one bottle of water is $1.39.

Upon substituting B=1.39 in equation (2) we will get,

`4*1.39+C=7.15`

`5.56+C=7.15`

Upon subtracting 5.56 from both sides of our equation we will get,

`5.56-5.56+C=7.15-5.56`

`C=1.59`

Therefore, the cost of each coffee is $1.59.