Eggs are expensive. If eggs had cost x less per dozen, it would have cost 40 cents less for 40eggs than if they

dozen

#1

Eggs are expensive. If eggs had cost x less per dozen, it would have cost 40 cents less for 40 eggs than if they had cost x cents more per dozen. Find x

Answer:

Let p be the actual price per dozen eggs.

“If eggs cost x cents less” means (p - x).
“If eggs cost x cents more” means (p + x).

Now the price is per dozen, but you’re buying 40 eggs… 40/12 = 3 1/3 dozen (or 10/3 dozen). So if eggs were x cents less, the price for 40 eggs would be

(10/3)(p - x)

And if eggs were x cents more, then the price for 40 eggs would be

(10/3)(p + x)

The cost for the eggs at the lower price (p-x) would be 40 cents less than the cost of the eggs at the higher price. So…

(10/3)(p - x) = (10/3)(p + x) - 0.40
(10/3)p - (10/3)x = (10/3)p + (10/3)x - 0.40
-(10/3)x = (10/3)x - 0.40
0 = (10/3)x + (10/3)x - 0.40
0.40 = (20/3)x
.06 = x

So x is 6 cents.