Question

Good evening can you help me please, it's for a DM tomorrow!!! "Okare" stones are precious stones whose value (in euros) is equal to the square of their mass (in grams). Unfortunately, a 20-gram "okaré" stone was dropped; It then broke into two pieces. 1. Prove that if one of the two pieces weighs 13

Answer 1

Let's assume that one of the two pieces weighs 13 grams, and the other piece weighs x grams. Then we can write:

20 = 13 + x (since the sum of the two pieces should be equal to the original weight of the stone)

Squaring both sides, we get:

400 = 169 + 26x + x^2

Simplifying, we get:

x^2 + 26x - 231 = 0

We can now use the quadratic formula to solve for x:

x = (-26 ± sqrt(26^2 - 4(1)(-231))) / 2(1)

x = (-26 ± sqrt(1376)) / 2

x = (-26 ± 37.07) / 2

x = 5.54 or x = -31.54

Since the mass of the second piece cannot be negative, it follows that x = 5.54 grams.

Therefore, if one of the two pieces weighs 13 grams, then the other piece weighs 5.54 grams. We can now check that the sum of the two pieces is indeed equal to the original weight of the stone:

13 + 5.54 = 18.54

And we can also calculate the value of each piece:

Value of the 13-gram piece = 13^2 = 169 euros

Value of the 5.54-gram piece = 5.54^2 = 30.7 euros

The total value of the two pieces is:

169 + 30.7 = 199.7 euros

We can see that the total value of the two pieces is less than the value of the original stone, which was:

20^2 = 400 euros

This is due to the fact that the stone lost some of its mass when it broke into two pieces.