Question

За 15 открыток,10 конвертов и блокнот заплатили 36 р. конверт в 4 раза дешевле блокнота на 50 копеек дороже открытки. сколько стоит открытка, блокнот, и конверт

Answer 1

Конверт  х , открытка -  х-50
блокнот 4х
 36р=3600 коп
15(х-50)+10х+1*4х=3600
15х-750+10х+4х=3600
29х=4350
х=150 коп. = 1,5 руб стоит конверт 
150-50=100 коп = 1 руб стоит открытка
150*4=600 коп=6 руб стоит блокнот

проверим 6+15 +15=36 руб

Answer 2

Пусть блокнот стоит х р, тогда конверт стоит х\4 р, а открытка (х\4-0,5) рублей.
Составим уравнение:
15(х\4-0,5)+10*х\4+х=36
3,75х-7,5+2,5х+х=36
7,25х=43,5
х=6. Цена блокнота 6 руб
6:4=1,5. Цена конверта 1,5 руб.
1,5-0,5=1. Цена открытки 1 руб.

Answer 3

Problem Analysis

We are given the following information: - The total cost of 15 postcards, 10 envelopes, and a notebook is 36 rubles. - The cost of an envelope is 4 times cheaper than the notebook. - The cost of an envelope is 50 kopeks more expensive than a postcard.

We need to find the individual prices of a postcard, an envelope, and a notebook.

Solution

Let's assign variables to the unknown prices: - Let p be the price of a postcard. - Let e be the price of an envelope. - Let n be the price of a notebook.

From the given information, we can form the following equations: 1. The total cost of 15 postcards, 10 envelopes, and a notebook is 36 rubles: - 15p + 10e + n = 36

2. The cost of an envelope is 4 times cheaper than the notebook: - e = n/4

3. The cost of an envelope is 50 kopeks more expensive than a postcard: - e = p + 0.50

We can solve this system of equations to find the values of p, e, and n.

Solution Steps

1. Substitute the value of e from equation 2 into equation 1: - 15p + 10(n/4) + n = 36

2. Simplify equation 1: - 15p + 10n/4 + n = 36

3. Multiply equation 1 by 4 to eliminate the fraction: - 60p + 10n + 4n = 144

4. Combine like terms in equation 3: - 60p + 14n = 144

5. Substitute the value of e from equation 3 into equation 2: - n/4 = p + 0.50

6. Simplify equation 2: - n = 4p + 2

7. Substitute the value of n from equation 6 into equation 4: - 60p + 14(4p + 2) = 144

8. Simplify equation 4: - 60p + 56p + 28 = 144

9. Combine like terms in equation 4: - 116p + 28 = 144

10. Subtract 28 from both sides of equation 4: - 116p = 116

11. Divide both sides of equation 4 by 116: - p = 1

Now that we have the value of p, we can substitute it back into equation 6 to find the value of n: - n = 4(1) + 2 - n = 6

Finally, we can substitute the values of p and n into equation 3 to find the value of e: - e = 1 + 0.50 - e = 1.50

Solution Summary

Based on the given information, the price of a postcard is 1 ruble, the price of an envelope is 1.50 rubles, and the price of a notebook is 6 rubles.

Answer: - The price of a postcard is 1 ruble. - The price of an envelope is 1.50 rubles. - The price of a notebook is 6 rubles.