Question

Equation 1: x (number of donuts) + y (number of cookies) = 15 (total items)

Equation 2: 1x (cost of each donut) + 1.5y (cost of each cookie) = 18 (total cost in dollars)

to find the values of x and y that satisfy both equations.

Answer 1

To solve the system of equations, isolate one variable from the first equation, then substitute it into the second equation to find the value of the other variable. In this case, solving gives us x = 9 donuts and y = 6 cookies.

Step-by-step explanation:

The question asks us to solve a system of linear equations to find the number of donuts (x) and cookies (y) a student can buy given the total number of items and the total cost. We can use substitution or elimination methods to solve it. To do this, we will work through the given equations step by step:

Step-by-Step Solution

Equation 1: x + y = 15 (Total items equation)

Equation 2: x + 1.5y = 18 (Total cost equation)

Step 1: Isolate one variable, for example x, from the first equation:

x = 15 - y

Step 2: Substitute the expression for x into the second equation:

15 - y + 1.5y = 18

Simplify the equation to find y:

0.5y = 3

y = 6

Step 3: Substitute the value of y back into the first equation to find x:

x = 15 - y

x = 15 - 6

x = 9

Thus, the student can buy 9 donuts and 6 cookies.