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

Answer:

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,  

$x=\frac{31-2y}{8}$

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

$3(\frac{(31-2y)}{8})+3y=17.25$

Upon distributing 3 we will get,

$\frac{93-6y}{8}+3y=17.25$

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

$\frac{93-6y}{8}+\frac{8*3y}{8}=17.25$  

$\frac{93-6y+24y}{8}=17.25$  

$\frac{93+18y}{8}=17.25$  

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

$8*\frac{93+18y}{8}=8*17.25$  

$93+18y=138$  

$18y=138-93$  

$18y=45$

$y=\frac{45}{18}=2.5$

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.

$8x+2*2.5=31$

$8x+5=31$

$8x=31-5$

$8x=26$

$x=\frac{26}{8}=3.25$

Therefore, the price of each coffee is $3.25.