Respuesta :
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: [tex]8x+2y=31...(1)[/tex]
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: [tex]3x+3y=17.25...(2)[/tex]
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,
[tex]x=\frac{31-2y}{8}[/tex]
Now let us substitute x's value in equation 2.
[tex]3(\frac{(31-2y)}{8})+3y=17.25[/tex]
Upon distributing 3 we will get,
[tex]\frac{93-6y}{8}+3y=17.25[/tex]
Now we will make a common denominator on left side of our equation.
[tex]\frac{93-6y}{8}+\frac{8*3y}{8}=17.25[/tex]
[tex]\frac{93-6y+24y}{8}=17.25[/tex]
[tex]\frac{93+18y}{8}=17.25[/tex]
Upon multiplying both sides of our equation by 8 we will get,
[tex]8*\frac{93+18y}{8}=8*17.25[/tex]
[tex]93+18y=138[/tex]
[tex]18y=138-93[/tex]
[tex]18y=45[/tex]
[tex]y=\frac{45}{18}=2.5[/tex]
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.
[tex]8x+2*2.5=31[/tex]
[tex]8x+5=31[/tex]
[tex]8x=31-5[/tex]
[tex]8x=26[/tex]
[tex]x=\frac{26}{8}=3.25[/tex]
Therefore, the price of each coffee is $3.25.
