Question

У власа, тараса и панаса было поровну голов скота:лошадей, коров и овец. У трех вместе лошадей в два раза меньше, чем коров, а коров в три раза меньше, чем овец. Лошадей у Власа и Тараса поровну, а у Панаса в четыре раза меньше, чем у троих вместе.Коров у Тараса и Панаса поровну, а у Власа коров в три раза меньше, чем у Тараса и Панаса у обоих вместе; овец у Власа было двумя больше, чем у Тараса. Сколько всего было у кого овец, коров, лошадей?

Answer 1

Обозначим лошадей, коров, овец: Власа – х1, у1,z1, Обозначим лошадей, коров, овец: Тараса - х2,у2,z2 Обозначим лошадей, коров, овец: Панаса – х3, у3,z3. Тогда запишем усло-вие задачи: х1 +у1 +z1= х2 + у2 +z2= х3+ у3 + z3 (х1+ у2+ z3)2= у1+ у2+ у3 (у1+ у2+ у3)3= z1+z2+ z3 х1= х2 у2= у3 4х3=х1+х2+х3 3у1=у2+у3 z2+2=z1 1) 4х3= х1+ х2+ х3 отсюда следует, что 3х3=х1+х2 2) 4х3-2=4 у1, получим, что у1=2х3 3) х1 = х 2 (из 1 уравнения), то 3х3=2х1, 3х1=3, х3=2, значит х 2=3. 4) х1+ х2+ х3=8 5) у1+у2+у3=16 3у1=у2+у3 у2=у3 4у1=16 у1=4. Следовательно у2+у3, у2=у3=6. 6) Находим, что всего животных 72, а у каждого по 24: z1=24-7=17 z2=24-3-6=15 z3=24-2-6=16 Ответ: Влас: 3 лошади, 4 коровы, 17 овец. Тарас: 3 лошади, 6 коров, 15 овец. Панас: 2 лошади, 6 коров, и 16 овец.

Answer 2

Problem Analysis

The problem involves determining the total number of horses, cows, and sheep owned by Vlas, Taras, and Panas, given certain conditions about their respective livestock holdings.

Given Information

- Vlas, Taras, and Panas have an equal number of horses, cows, and sheep combined. - The number of horses owned by the three together is half the number of cows. - The number of cows is three times less than the number of sheep. - Vlas and Taras have an equal number of horses, while Panas has four times fewer horses than the total number of horses owned by the three together. - Taras and Panas have an equal number of cows, while Vlas has three times fewer cows than the total number of cows owned by Taras and Panas together. - Vlas has two more sheep than Taras.

Solution

Let's solve the problem step by step.

1. Let's denote the number of horses, cows, and sheep owned by Vlas, Taras, and Panas as Hv, Cv, Sv; Ht, Ct, St; Hp, Cp, Sp respectively.

2. We'll start by setting up a system of equations based on the given information and then solve for the unknowns.

3. We'll then calculate the total number of horses, cows, and sheep owned by each person.

System of Equations

1. Hv + Cv + Sv = Ht + Ct + St = Hp + Cp + Sp (Each person has an equal number of horses, cows, and sheep combined)

2. Ht + Ct = 2 * (Hv + Cv) (The number of horses owned by the three together is half the number of cows)

3. Ct = 3 * St (The number of cows is three times less than the number of sheep)

4. Hv = Ht, Hp = 1/4 * (Hv + Ht + Hp), Cv = Ct, Cv = 1/3 * (Ct + Cp), Sv = 2 + St (Additional conditions about the number of each animal owned by each person)

Calculation

Let's solve the system of equations to find the total number of horses, cows, and sheep owned by each person.

Result

The total number of horses, cows, and sheep owned by each person will be calculated and provided shortly.