Question

Соки яблочный и вишневый продаются в пакетах с одинаковыми крышечками. Магазин устроил акцию: 4 крышечки от сока можно обменять на полный пакет яблочного сока, а 8 крышечек— на полный пакет вишневого сока. Вася собрал 40 крышечек от сока и решил поучаствовать в этой акции, обменивая крышечки на пакеты сока. Получая при обмене полный пакет сока, он выпивал сок, а крышечку от него использовал при следующих обменах. В конце концов, когда он выпил последний пакет сока, у него осталась всего одна крышечка. Сколько пакетов сока выпил Вася, участвуя в этой акции?

Answer 1

Если осталась одна крышка перед этим была 6 или 8( их обменяли и сок выпили) заметим что 40 крышек можно обменять на 6 яблочных и 2 вишневых либо на 4 вишневых и 2 яблочных тогда в первом случае Вася выпил 6+2+1=9 соков а во втором 4+2+1=7 соков

Answer 2

Problem Analysis

To solve this problem, we need to determine how many packets of juice Vasya drank while participating in the promotion. Vasya collected 40 juice caps and exchanged them for full juice packets. Each time he received a full packet, he drank the juice and used one cap for the next exchange. At the end of the promotion, he had only one cap left. We need to find the number of juice packets Vasya drank during the promotion.

Solution

Let's assume Vasya exchanged x caps for apple juice packets and y caps for cherry juice packets. We can set up the following equations based on the given information:

1. Vasya exchanged 4 caps for each apple juice packet, so the number of apple juice packets he received is x/4. 2. Vasya exchanged 8 caps for each cherry juice packet, so the number of cherry juice packets he received is y/8. 3. Vasya collected a total of 40 caps, so the total number of caps exchanged is x + y.

We can now set up the equation:

x/4 + y/8 = 40 - 1

Simplifying the equation:

2x + y = 312

To find the number of juice packets Vasya drank, we need to find the value of x.

Solving the Equation

To solve the equation 2x + y = 312, we can use trial and error or substitution. Let's use trial and error to find the value of x.

Let's start with x = 1 and check if it satisfies the equation:

2(1) + y = 312 2 + y = 312 y = 312 - 2 y = 310

Since y is not a multiple of 8, x = 1 is not a valid solution.

Let's try x = 2:

2(2) + y = 312 4 + y = 312 y = 312 - 4 y = 308

Since y is not a multiple of 8, x = 2 is not a valid solution.

Let's continue this process until we find a valid solution.

After trying a few values, we find that x = 8 and y = 296 is a valid solution:

2(8) + 296 = 312

Therefore, Vasya exchanged 8 caps for apple juice packets and 296 caps for cherry juice packets.

Calculating the Number of Juice Packets

Now that we know the values of x and y, we can calculate the number of juice packets Vasya drank.

The number of apple juice packets Vasya received is x/4 = 8/4 = 2.

The number of cherry juice packets Vasya received is y/8 = 296/8 = 37.

Therefore, Vasya drank 2 apple juice packets and 37 cherry juice packets while participating in the promotion.

Answer

Vasya drank a total of 2 apple juice packets and 37 cherry juice packets while participating in the promotion.