algebra-precalculus
If a cake is cut into $5$ equal pieces, each piece would be $80$ grams
heavier than when the cake is cut into $7$ equal pieces. How heavy is
the cake?
How would I solve this problem? Do I have to try to find an algebraic expression for this? $5x = 7y + 400$?
Along the lines of this discussion, I've arrived at the following packing:
I've added the following lines of Javascript to function doRender() in RectanglePacker:
(notice that I scaled down all dimensions by a factor of 10)
params.canvasWidth = 321;
params.canvasHeight = 221;
var b = []
var i = 0;
var bi = 0;
b[i++] = { w: 180, h: 120, n: 5 };
b[i++] = { w: 60, h: 80, n: 14 };
b[i++] = { w: 40, h: 50, n: 15 };
b[i++] = { w: 90, h: 50, n: 10 };
for (var j=0; j<b.length; j++) {
for (var n=0; n<b[j].n; n++) {
blocks[bi++] = { w: b[j].w, h: b[j].h };
}
}
If you bend the $60$-inch wire into a square, the area should be $\left( \frac{60}4\right)^2=225$
In general, we have
$$\left( p+q\right)^2 \ne p^2+q^2$$
Hence $p=\frac{24}4$ and $q=\frac{36}{4}$
We have $(p+q)^2 = p^2+2pq+2^2$. Hence there should be a difference of $2pq=2\left( \frac{24}{4}\right)\left(\frac{36}{4} \right)=108.$
Geometrically: Don't forget the rectangle region.
Best Answer
If cut it into 5 pieces, but decide you wanted 7 instead, so you cut away 80 grams from each slice, and make two (not so pretty) pieces from that. Now you have 7 pieces of equal size, which means you've got 400g evenly divided among the two ugly out of the seven pieces, so the whole cake weighted 1400g.