Question

On Monday Harold picked up four donuts and two large coffees for the office staff. He paid 4.08. On Tuesday Melinda picked up two donuts and three large coffees and paid 3.92. What is the cost of one donut? What is the cost of one large coffee?

Answer 1

One way to look at this is to make 2 equations and treat it as a set of equations. We will make the cost of a donut equal to x, and the cost of a coffee equal to y.

Harold's order:
4x + 2y = 4.08

Melinda's order:
2x + 3y = 3.92

To combine these equations, we need to cancel out either x or y:
4x + 2y = 4.08
2x + 3y = 3.92

4x + 2y = 4.08
4x + 6y = 7.84

4x + 2y = 4.08
-4x - 6y = -7.84

We can now combine these equations:
4x + 2y = 4.08
-4x - 6y = -7.84

-4y = -3.76

y = 0.94

Therefore the cost of a large coffee is $0.94. We can plug this into either original equation to find the cost of a donut.
4x + 2y = 4.08
4x + 2(0.94) = 4.08
4x + 1.88 = 4.08
4x = 2.20
x = 0.55

The cost of a donut is $0.55, and the cost of a large coffee is $0.94.