Упр.1106 ГДЗ Ткачёва 5 класс (Математика)

1) 42 : (х + 9) = 35 : 8; 2) 18 : 5 = (х — 4) : 10;
3) (5 · x — 6) : 12 = 44 : 3; 4) 39 : 8 = 26 : (х : 4 — 1).

1) $$42 : (x + 9) = 35 : 8$$

Перемножим крайние и средние члены пропорции:

$$35(x + 9) = 42 \cdot 8$$

$$35(x + 9) = 336$$

$$x + 9 = \frac{336}{35} = \frac{48}{5} = 9 \frac{3}{5}$$

$$x = 9 \frac{3}{5} — 9 = \frac{3}{5}$$

2) $$18 : 5 = (x — 4) : 10$$

$$5(x — 4) = 18 \cdot 10$$

$$5(x — 4) = 180$$

$$x — 4 = \frac{180}{5} = 36$$

$$x = 36 + 4 = 40$$

3) $$(5 \cdot x — 6) : 12 = 44 : 3$$

$$3(5x — 6) = 12 \cdot 44$$

$$3(5x — 6) = 528$$

$$5x — 6 = \frac{528}{3} = 176$$

$$5x = 176 + 6 = 182$$

$$x = \frac{182}{5} = 36 \frac{2}{5}$$

4) $$39 : 8 = 26 : (x : 4 — 1)$$

$$39(x : 4 — 1) = 8 \cdot 26$$

$$39(x : 4 — 1) = 208$$

$$x : 4 — 1 = \frac{208}{39} = \frac{16}{3} = 5 \frac{1}{3}$$

$$x : 4 = 5 \frac{1}{3} + 1 = 6 \frac{1}{3} = \frac{19}{3}$$

$$x = \frac{19}{3} \cdot 4 = \frac{76}{3} = 25 \frac{1}{3}$$

Ответ

1) $$\frac{3}{5}$$; 2) $$40$$; 3) $$36 \frac{2}{5}$$; 4) $$25 \frac{1}{3}$$.