Question

У Винтика и Шпунтика в копилках лежат монеты. У каждого только одного достоинства. Если Винтик отдаст 5 своих монет, а Шпунтик 6 своих, то они смогут купить самокат за 70 рублей. А если Шпунтик отдаст 7 монет, а Винтик 6, то они смогут купить самокат с пропеллером за 83 рублей. Мальчики решили вложить по одинаковому количеству монет на покупку велосипеда с пропеллером за 91 рубль. По сколько монет должны дать Винтик и Шпунтик?

Answer 1

Ответ:

По 7 и 8 монет должны дать

Answer 2

Problem Analysis

We have two characters, Vintik and Shpuntik, who each have a certain number of coins in their piggy banks. They want to buy different items, and we are given two scenarios with different combinations of coins that they can contribute to purchase these items. We need to determine how many coins each of them should contribute to buy a bicycle with a propeller for 91 rubles.

Solution

Let's solve this problem step by step.

1. In the first scenario, Vintik gives away 5 coins and Shpuntik gives away 6 coins to buy a scooter for 70 rubles. 2. In the second scenario, Shpuntik gives away 7 coins and Vintik gives away 6 coins to buy a scooter with a propeller for 83 rubles. 3. In both scenarios, the number of coins contributed by Vintik and Shpuntik is equal. 4. We need to find the number of coins each of them should contribute to buy a bicycle with a propeller for 91 rubles.

Let's assume that Vintik contributes x coins and Shpuntik contributes x coins.

According to the first scenario: - Vintik contributes 5 coins, so he has x - 5 coins left. - Shpuntik contributes 6 coins, so he has x - 6 coins left. - The total amount they have is (x - 5) + (x - 6) = 2x - 11 coins. - They can buy a scooter for 70 rubles, so the value of each coin is 70 / (2x - 11) rubles.

According to the second scenario: - Shpuntik contributes 7 coins, so he has x - 7 coins left. - Vintik contributes 6 coins, so he has x - 6 coins left. - The total amount they have is (x - 7) + (x - 6) = 2x - 13 coins. - They can buy a scooter with a propeller for 83 rubles, so the value of each coin is 83 / (2x - 13) rubles.

Since they want to buy a bicycle with a propeller for 91 rubles, the value of each coin in this scenario is 91 / (2x - 13) rubles.

We can set up the following equation to find the value of x:

(70 / (2x - 11)) = (91 / (2x - 13))

Solving this equation will give us the value of x, which represents the number of coins each of them should contribute.

Let's solve this equation:

(70 / (2x - 11)) = (91 / (2x - 13))   # Cross-multiplication
70(2x - 13) = 91(2x - 11)             # Distributive property
140x - 910 = 182x - 1001               # Simplify
42x = 91                            # Combine like terms
x = 91 / 42                        # Divide both sides by 42
x ≈ 2.17                           # Approximate the value of x

Since we can't have a fraction of a coin, we need to round the value of x to the nearest whole number. Therefore, Vintik and Shpuntik should each contribute 2 coins to buy the bicycle with a propeller for 91 rubles.

Answer

Vintik and Shpuntik should each contribute 2 coins to buy the bicycle with a propeller for 91 rubles.