Question

(Старинная задача)а)Сколько надо взять карамели по цене 16руб. за 1кг и по цене 9руб. за 1кг,чтобы составить 21кг смеси по цене 11руб. за килограмм.б)Для вышивания приобрели мулине двух сортов:по цене 5руб. и 11руб.40коп. за моток, всего 32 мотка.Сколько мотков того и другого сорта было приобретено,если в среднем один моток обошелся по 9 руб.

Answer 1

5х+11.40*(32-х)=32*9, 5х+364.8-11.40х=288, 6.4х=76.8, х=76.8:6.4, х=12 (м)-приобрели по 5 рублей. 
32-12=20 (м)-приобрели по 11р 40копейки

Answer 2

Problem a)

To solve this problem, we can set up a system of equations based on the given information.

Let's assume that x kilograms of candy at 16 rubles per kilogram and y kilograms of candy at 9 rubles per kilogram are needed to make a 21-kilogram mixture at 11 rubles per kilogram.

The first equation represents the total weight of the mixture: x + y = 21

The second equation represents the total cost of the mixture: 16x + 9y = 11 * 21

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 the first equation, we can express x in terms of y: x = 21 - y

Substituting this value of x into the second equation: 16(21 - y) + 9y = 11 * 21 336 - 16y + 9y = 231 -7y = -105 y = 15

Substituting the value of y back into the first equation: x + 15 = 21 x = 6

Therefore, we need 6 kilograms of candy at 16 rubles per kilogram and 15 kilograms of candy at 9 rubles per kilogram to make a 21-kilogram mixture at 11 rubles per kilogram.

Answer: a) We need 6 kilograms of candy at 16 rubles per kilogram and 15 kilograms of candy at 9 rubles per kilogram to make a 21-kilogram mixture at 11 rubles per kilogram.

Problem b)

To solve this problem, we can set up a system of equations based on the given information.

Let's assume that x motoks of thread at 5 rubles per motok and y motoks of thread at 11 rubles and 40 kopeks per motok were purchased, with a total of 32 motoks.

The first equation represents the total number of motoks: x + y = 32

The second equation represents the total cost of the motoks: 5x + 11.40y = 9 * 32

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 the first equation, we can express x in terms of y: x = 32 - y

Substituting this value of x into the second equation: 5(32 - y) + 11.40y = 9 * 32 160 - 5y + 11.40y = 288 6.40y = 128 y = 20

Substituting the value of y back into the first equation: x + 20 = 32 x = 12

Therefore, 12 motoks of thread at 5 rubles per motok and 20 motoks of thread at 11 rubles and 40 kopeks per motok were purchased.

Answer: b) 12 motoks of thread at 5 rubles per motok and 20 motoks of thread at 11 rubles and 40 kopeks per motok were purchased.