Question

За 3 линейки и 1 угольник заплатили 112 руб.,а за 1 линейку и 3 угольника заплатили 224 руб.Сколько стоит 1 линейка и 1 угольник?

Answer 1

Пусть У руб стоимость угольника, Х руб стоимость линейки.

Решаем системой уравнений
3Х+У=112
Х+3У=224

3Х+У=112
Х+3У=224 I *(-3)

3Х+У=112
-3Х-9У=-672

-8У=-672+112

-8У=-560
У=-560:(-8)
У=70 руб стоимость угольника
3Х+70=112
3Х=112-70
3Х=42
Х=14 руб стоимость линейки

Answer 2

Problem Analysis

We are given the information that for 3 lines and 1 triangle, the cost is 112 rubles, and for 1 line and 3 triangles, the cost is 224 rubles. We need to find the cost of 1 line and 1 triangle.

Solution

Let's assume the cost of 1 line is x rubles and the cost of 1 triangle is y rubles.

From the given information, we can set up the following equations:

Equation 1: 3x + y = 112 (for 3 lines and 1 triangle) Equation 2: x + 3y = 224 (for 1 line and 3 triangles)

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using the method of substitution:

From Equation 1, we can express y in terms of x: y = 112 - 3x

Substituting this value of y into Equation 2: x + 3(112 - 3x) = 224 x + 336 - 9x = 224 -8x = -112 x = 14

Now, substituting the value of x back into Equation 1 to find y: 3(14) + y = 112 42 + y = 112 y = 70

Therefore, the cost of 1 line is 14 rubles and the cost of 1 triangle is 70 rubles.

Answer

The cost of 1 line and 1 triangle is 14 rubles and 70 rubles respectively.