The mass of three teaspoons and two forks is 360g. Find the mass of a teaspoon if the mass

The mass of three teaspoons and two forks is 360g. Find the mass of a teaspoon if the mass of three forks is less than the mass of five teaspoons by 30g.

1) Let the mass of one teaspoon be x grams, and one fork – y grams.

2) Then (3x + 2y) is the mass of three spoons and two forks, which is 360 grams.

3) 3 grams – the mass of three forks, 5x grams – the mass of five spoons.

4) By condition, the mass of three forks is 30 grams less than the mass of five spoons, which means that

5x – 3y = 30.

5) Let’s compose and solve the system of equations:

3x + 2y = 360;

5x – 3y = 30;

9x + 6y = 1080;

10x – 6y = 60;

9x + 6y + 10x – 6y = 1080 + 60;

19x = 1140;

x = 1140: 19;

x = 60.

6) We get that x = 60 grams is the mass of one teaspoon.

Answer: 60 grams.