B2. An Arab had 1000 gold coins. He divided them among his three sons and four daughters. All the sons received equal shares. The daughters also received equal shares, each half as much as each of the brothers.

a) How many gold coins did each son receive?

b) How many gold coins did each daughter receive?

c) How many gold coins would each child receive if the division were equal? Round the result down.
B2. If we denote the share of each of the sons with $x$, and the share of each of the daughters with $y$, we have: $3 x+4 y=$ 1000. From the text, we understand that each of the daughters received half as much as each of the brothers, which can be written as $y=\frac{x}{2}$. If we take this relationship into account in the previously written equation, we get a linear equation with one unknown: $3 x+4 \frac{x}{2}=1000$ or $3 x+2 x=1000$, from which we can calculate $x=200$. Each son received 200 gold coins.

Considering that each of the daughters received half as much as each of the sons: $y=\frac{x}{2}=100$. Each daughter received 100 gold coins.

If the division were equal, each of the seven children would receive an equal share: $1000: 7=$ 142.86. When rounded down, we get 142. In an equal division, each child would receive 142 gold coins.

## Scoring: Total: 5 points

a) Choosing the unknown and setting up the equation, e.g., $x+x+x+\frac{x}{2}+\frac{x}{2}+\frac{x}{2}+\frac{x}{2}=1000 \ldots 1 \mathbf{t}$

![](https://cdn.mathpix.com/cropped/2024_06_07_a1c9447e499e971c849bg-6.jpg?height=49&width=1536&top_left_y=2144&top_left_x=366)
Written answer, e.g., Each son receives 200 gold coins. .................................. 1 t

b) Written answer, e.g., Each daughter receives 100 gold coins. ............................... 1 t

c) Written answer, e.g., In an equal division, each child would receive 142 gold coins. $1 \mathrm{t}$