I’m almost 50, and to me, mathematics has always been contrived number games based on a deeper logic always beyond my grasp. Yet through my interests in physics, IT, music and astronomy, I know that mathematics is an amazingly adaptable language which can be used to express (and therefore model) any process in the universe one cares to apply it to.

The “Pizza + Donut” quiz in Basic Mathematics is a perfect example of the mathematical logic which has confounded me since childhood. I fervently wish, with all my heart, that I could follow the logic in the statement: “If a pizza costs $10.50 more than a donut, then a pizza and a donut must cost $10.50 more than two donuts.” I absolutely cannot fathom the logic behind that statement. Why two donuts? If we don’t know the cost of one donut, how can we possibly say the difference between a pizza and donut combined is 10.50 more than two donuts?

Please, please, can someone help me follow that logic? I believe if I could only grasp it, a new understanding of this universe would be unlocked for me.

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TopNewestLet \(P \) and \(D\) denote the price of a pizza and a donut (in $), respectively.

The first part of the sentence says that \(P = 10.50 + D\).

Now, if we add \(D\) to both sides of this equation, we will get \(P + D = 10.50 + 2D\).

What does \(P+D\) and \(10.50 + 2D\) represents?

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OK, I see how you can turn the statement into an equation - and it does make it easier to think about! So now I can see why you might put two donuts on the right side of the equation if you add one to the left. Great - progress! But in trying to solve for D, I just can’t reason it out; I don’t know what it represents.

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You can't solve for \(D\) because you are only given 1 (linear) equation with 2 variables.

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No. Just because you don't have enough information to solve an equation (or multiple equation) doesn't automatically makes the question flawed.

Try more problems. You'll get a hang of it! ;)

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Wow. That is one expensive donut

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