Help please - Quadratic?

Rite, I did A2 Maths this summer, and am helping a student with GCSE and would love to know how to do this question. Any help would be greatly appreciated. And yes I am embarassed that I can't see the damn answer.

Problemo:

A farmer makes a profit of x cents on each of the "x+5" eggs her hen lays. If her total profit was 84 cents, find the number of eggs the hen lays.

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Yes that's really it. Thank you.

Reply 1

jpowell

The farmer has x + 5 eggs, and each egg makes a profit of x cents, so x*(x+5) = 84

It's a simple quadratic.

x^2 + 5x - 84 = 0
(x - 7)(x+12) = 0

We take the positive solution, so x = 7 cents

Reply 2

Kolya

\large x(x+5)=84 \\ x^2+5x=84 \\ x^2+5x-84=0 \\ (x+12)(x-7) = 0

The hen lays 7 eggs.

Reply 3

AAJ1

Thank you both. I thought I was going mad, because the answer in the back of the book says 12 eggs.

They are obviously hopelessly wrong.

Reply 4

DDCA

AAJ1

Thank you both. I thought I was going mad, because the answer in the back of the book says 12 eggs.

They are obviously hopelessly wrong.

Read the question carefully. What does x represents? What is the expression that represents the number of eggs? :smile:

Reply 5

jpowell

The hen lays 12 eggs, that are 7 cents each.

Reply 6

FaSaMa03

Original post by jpowell

The farmer has x + 5 eggs, and each egg makes a profit of x cents, so x*(x+5) = 84

It's a simple quadratic.

x^2 + 5x - 84 = 0
(x - 7)(x+12) = 0

We take the positive solution, so x = 7 cents