Question

Kathryn buys 8 cups of coffee and 2 bagels one day and pays $31. Harry buys 3 cups of coffee and 3 bagels the same day and pays $17.25. How much is each cup of coffee and each bagel

Answer 1

Each coffee= $3.25

Each bagel= $2.5

Step-by-step explanation:

Let x be price of each cup of coffee and y be the price of each bagel.

We have been given that Kathryn buys 8 cups of coffee and 2 bagels one day and pays $31. We can represent this information in an equation as:
`8x+2y=31...(1)`

We are also told that Harry buys 3 cups of coffee and 3 bagels the same day and pays $17.25. We can represent this information in an equation as:
`3x+3y=17.25...(2)`

Using our given information we have a formed a system of equations and we will solve our system of equations using substitution method.

From equation 1 we will get,

`x=(31-2y)/(8)`

Now let us substitute x's value in equation 2.

`3(((31-2y))/(8))+3y=17.25`

Upon distributing 3 we will get,

`(93-6y)/(8)+3y=17.25`

Now we will make a common denominator on left side of our equation.

`(93-6y)/(8)+(8*3y)/(8)=17.25`

`(93-6y+24y)/(8)=17.25`

`(93+18y)/(8)=17.25`

Upon multiplying both sides of our equation by 8 we will get,

`8*(93+18y)/(8)=8*17.25`

`93+18y=138`

`18y=138-93`

`18y=45`

`y=(45)/(18)=2.5`

Therefore, price of each bagel is $2.5.

Now let us substitute y=2.5 in equation 1 to find the price of each coffee.

`8x+2*2.5=31`

`8x+5=31`

`8x=31-5`

`8x=26`

`x=(26)/(8)=3.25`

Therefore, the price of each coffee is $3.25.