Question

В парке были посажены тополя,ели,сосны и чинары.Количество тополей составляет 3/4 количества елей и 6/5 количества сосен.Количество сосен составляет 1/6 количества всех деревьев.Сколько чинар посадили,если всего было посажено 90 деревьев?

Answer 1

90*1/6=15 (сосен)
15*6/5=18 (тополи)
18:3/4=24 (ели)
90-(15+18+24)=90-57=33
Ответ: посадили 33 чинары

Answer 2

Problem Analysis

We are given information about the types of trees planted in a park: poplars, spruces, pines, and plane trees. We are also given the ratios of the number of poplars to the number of spruces and pines, as well as the ratio of the number of pines to the total number of trees. We need to determine the number of plane trees planted in the park.

Solution

Let's assign variables to the unknown quantities: - Let P represent the number of poplars. - Let S represent the number of spruces. - Let N represent the number of pines. - Let C represent the number of plane trees.

From the given information, we can form the following equations: 1. The number of poplars is 3/4 of the number of spruces: P = (3/4)S. 2. The number of poplars is 6/5 of the number of pines: P = (6/5)N. 3. The number of pines is 1/6 of the total number of trees: N = (1/6)(P + S + N + C). 4. The total number of trees is 90: P + S + N + C = 90.

We can solve this system of equations to find the values of P, S, N, and C.

Solution Steps

1. Substitute equation 1 into equation 2 to eliminate P: - (3/4)S = (6/5)N - Simplifying, we get: S = (8/5)N. 2. Substitute equations 1 and 2 into equation 3 to eliminate P and N: - (1/6)(P + S + N + C) = N - Substitute P = (3/4)S and N = (6/5)S: - (1/6)((3/4)S + S + (6/5)S + C) = (6/5)S - Simplifying, we get: (1/8)S + (1/6)C = (6/5)S. 3. Substitute equations 1, 2, and 3 into equation 4 to eliminate P, S, and N: - (3/4)S + S + (6/5)S + C = 90 - Simplifying, we get: (47/20)S + C = 90. 4. Rearrange equation 2 to solve for N: - N = (5/6)(P + S + N + C) - Substitute P = (3/4)S: - N = (5/6)((3/4)S + S + N + C) - Simplifying, we get: (1/8)S + (1/6)N + (1/6)C = N. 5. Substitute equation 1 into equation 4 to eliminate P: - (3/4)S + S + (6/5)S + C = 90 - Substitute P = (3/4)S: - (3/4)S + S + (6/5)S + C = 90 - Simplifying, we get: (47/20)S + C = 90. 6. Substitute equation 5 into equation 4 to eliminate N: - (1/8)S + (1/6)N + (1/6)C = N - Substitute N = (6/5)S: - (1/8)S + (1/6)((6/5)S) + (1/6)C = (6/5)S - Simplifying, we get: (1/8)S + (1/5)S + (1/6)C = (6/5)S. 7. Solve the system of equations formed in steps 3, 5, and 6 to find the values of S and C. 8. Substitute the values of S and C into equation 1 to find the value of P. 9. Substitute the values of P, S, and C into equation 4 to find the value of N. 10. Finally, substitute the values of P, S, N, and C into equation 4 to verify that the total number of trees is 90.

Let's perform these steps to find the solution.