Question

Срочно помогите пж решить задачу!!! :-( Две дюжины столовых ложек и три дюжину чайных ложек имеют массу 1,344 кг, а масса трёх дюжин таких же столовых и трёх дюжин таких же чайных ложек-1,872 кг. Найдите массу одной столовой ложки и одной чайной ложки (Ответ выразите в граммах.)

Answer 1

Дюжина - мера, равная 12.
Соответственно, 24 ст.л.+36 ч.л.=1,344 кг, 36 ст.л.+36 ч.л.=1,872 кг.
1) 1,872-1,344=0,528 кг весят 12 ст.л. (36-24=24)
2) 0,528:12=0,044 кг весит 1 ст.л.
х - вес 1 ч.л.
24*0,044+36х=1,344;
1,056+36х=1,344;
36х=0,288;
х=0,008
0,044 кг=44 г
0,008 кг=8 г
Ответ: столовая ложка весит 44 г, чайная - 8 г.

Answer 2

Problem Analysis

To solve this problem, we need to find the mass of one tablespoon and one teaspoon. We are given that two dozen tablespoons and three dozen teaspoons have a total mass of 1,344 kg, and the mass of three dozen tablespoons and three dozen teaspoons is 1,872 kg. We need to find the mass of one tablespoon and one teaspoon in grams.

Solution

Let's assume the mass of one tablespoon is x grams and the mass of one teaspoon is y grams.

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

Equation 1: 2x + 3y = 1,344 (mass of two dozen tablespoons and three dozen teaspoons) Equation 2: 3x + 3y = 1,872 (mass of three dozen tablespoons and three dozen teaspoons)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination to solve for x and y.

Multiplying Equation 1 by 3 and Equation 2 by 2, we get:

Equation 3: 6x + 9y = 4,032 Equation 4: 6x + 6y = 3,744

Subtracting Equation 4 from Equation 3, we eliminate x:

(6x + 9y) - (6x + 6y) = 4,032 - 3,744 3y = 288 y = 288 / 3 y = 96

Now, we substitute the value of y back into Equation 1 to find x:

2x + 3(96) = 1,344 2x + 288 = 1,344 2x = 1,344 - 288 2x = 1,056 x = 1,056 / 2 x = 528

Therefore, the mass of one tablespoon is 528 grams and the mass of one teaspoon is 96 grams.

Answer

The mass of one tablespoon is 528 grams and the mass of one teaspoon is 96 grams.