Write System of Equations from context

Question

Brianna went into a bakery and bought 2 cookies and 3 brownies, costing a total of $9.50. Nevaeh went into the same bakery and bought 10 cookies and 6 brownies, costing a total of $20.50. Write a system of equations that could be used to determine the price of each cookie and the price of each brownie. Define the variables that you use to write the system.

Answer 1

Hello, Ian,

We can write two equations based on the two purchases. Let X be the price of each cookie bought and Y the price of a brownie. Since we know how many of each were purchased, we can write expressions for both women:

Brianna: 2X + 3Y = 9.50 [i.e., 2 cookies at x each and 3 brownies at Y each cost a total of $9.50]

Nevah: 10X + 6Y = 20.50

I'll pick the first equation and rearrange it so that "X" is isolated:

X = (9.50 - 3Y)/2

Now substitute that definition of X into the second equation. That way we eliminate X from the equation altogether, and can solve for Y.

(10(9.50 - 3Y))/2 +6Y = 20.50

47.5 - 15Y + 6Y = 20.50

Y = $3

Each brownie costs $3. To find X, use this in either equation and solve for X:

2X + 3Y = 9.50

2X + 3(3) = 9.50

X = $0.25

Each cookie is a quarter.

Check by entering these values into either equation:

2(0.25) + 3(3) = 9.50 ?

Yes

Skip the brownies and for for the cookies.

Bob