## Task A-1.2.

Tea mixed a dough from three ingredients: flour, water, and eggs. The mass of flour in the dough to the mass of water is in the ratio of $7: 2$, while the mass of water to the mass of eggs is in the ratio of 5 : 2. The total mass of the dough is 1470 grams. Determine the mass of each ingredient.
## First solution.

Let's denote the masses of flour, water, and eggs by $x, y$, and $z$, respectively.

The given ratios can be represented as $x: y=7: 2=35: 10$ and $y: z=5: 2=10: 4$, i.e., as the ratio

$$
x: y: z=35: 10: 4
$$

1 point

Therefore, we can write $x=35 t, y=10 t \text{ and } z=4 t$, where $t$ is a positive real number. 1 point

The total mass is 1470 grams, i.e., $35 t + 10 t + 4 t = 1470$. 1 point

Thus, we have $49 t = 1470$, i.e., $t = 30$.

The total mass of flour is $35 t = 1050 \text{ g}$, water $10 t = 300 \text{ g}$, and eggs $4 t = 120 \text{ g}$.