This makes no sense

I just started and I'm stumped on the first donut problem. Not because it's hard, but because it makes no sense. It states that:
Pizza + Donut = $11.00
Pizza - Donut = $10.50
What is the cost of the donut?

My first thought is "It's obviously $0.50 becauseif the pizza is $11 with the donut and $10.5 without than the donut must be 0.5." But apparently I was wrong. The donut is somehow 0.25 and even with their explanation I can not come to a conclusion on how they got this answer. It makes zero sense.

#Algebra

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Comments

You're wrong.

If the price of the donut is $0.50, then
from the first equation, the price of the Pizza is $10.50;
from the second equation, the price of the Pizza is $11.00.

Which is absurd because the price of the pizza cannot be both $10.50 and $11.00 at the same time. So your conclusion is incorrect.

Pi Han Goh - 3 years, 7 months ago

You're right sorry. Dumb mistake on my part.

The Suited Hound - 3 years, 7 months ago

The reason this conclusion is incorrect comes from your assumption that the pizza is capable of having two different prices. Set donuts = d and pizzas = p, and solve the system of equations that results by converging the two:

p + d = 11.00

p - d = 10.50

(p + p) (d + -d) = (11.00 + 10.50)

2p = 21.50

p = 10.75

Now we know that 1 Pizza costs 10.75. Now, plug in p in one of the original equations to solve for d.

10.75 + d = 11.00

d = 11.00 - 10.75

d = 0.25

From this, we can gather that 1 Donut costs 0.25 (25 cents).

Hope this helped!

Hunter Edwards - 3 years, 7 months ago

Sorry! forgot to plug into the original equations to check my answer:

10.75 + 0.25 = 11.00 True!

10.75 - 0.25 = 10.50 True!

Thus, 1 Donut = 0.25, and 1 Pizza = 10.75.

Hunter Edwards - 3 years, 7 months ago

I know. I had another brilliant account when I was 6 and I had exactly 100% of the questions I tried to answer incorrect. Now, a year ago I returned to Brilliant with a different account and I still had the pizza/ donut one incorrect. :)

A Former Brilliant Member - 3 years, 7 months ago

lol

Sowmya Surapaneni - 3 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$