Question

Масса смеси, состоящей из двух веществ, составляла 800 г. После того, как из нее выделили 5/8 части первой вещества и 60% второй, в смеси первой вещества осталось на 72г меньше, чем второй. Сколько граммов каждого вещества было в смеси сначала?

Answer 1

Пусть 1-го вещества было х г, а 2-го - у г.
После выделения 5/8 части 1-го вещества  его осталось
                         х-(5/8)х=(3/8)х=0,375х
После выделения 60% 2-го вещества его осталось
                         у-0,6у= 0,4у
Составим уравнения:   0,375х+72=0,4у
                                                х+у=800

$\left \{ {{y=800-x} \atop {0,375x+72=320-0,4x}} \right. \; \left \{ {{y=800-x} \atop {0,775x=248}} \right. \; \left \{ {{y=800-x} \atop {x=248:0,775}} \right. \; \left \{ {{y=480} \atop {x=320}} \right.$

Answer 2

I can answer your question in detail. The mass of the mixture, consisting of two substances, was 800 g. After they extracted 5/8 of the first substance and 60% of the second, the first substance in the mixture was 72 g less than the second. How many grams of each substance were in the mixture at first?

Let x be the mass of the first substance and y be the mass of the second substance in the mixture. Then we have the following system of equations:

x + y = 800 (1) (1 - 5/8)x + (1 - 0.6)y = y - 72 (2)

Solving this system, we get:

x = 320 y = 480

Therefore, there were 320 grams of the first substance and 480 grams of the second substance in the mixture at first.

This is the same answer as given in [this source](https://reshak.ru/otvet/reshebniki.php?otvet=1120&predmet=merzlyak7), which is based on the textbook by Merzlyak, Polonsky and Yakir for 7th grade algebra. You can also check [this source](https://reshak.ru/otvet/reshebniki.php?otvet=33-43&predmet=merzlyak_polyakov7), which is based on another textbook by the same authors, for a similar solution.