Question

Купили 9 одинаковых ручек,11 одинаковых фломастеров и 7 одинаковых карандашей, заплатив 658 рублей. Какова цена ручки, если известно, что фломастер дороже карандаша на 14 рублей, но дешевле ручки на 12 рублей?

Answer 1

ручка-x

фломастер-x-12

карандаш-x-12-14

9x+11(x-12)+7(x-12-14)=658

9x+11x-132+7x-84-98=658

27x-314=658

27x=972

x=36

ответ:36р

Answer 2

Problem Analysis

To find the price of a pen, we need to determine the cost of each item (pen, marker, and pencil) based on the given information. We know that the marker is 14 rubles more expensive than the pencil, and the pen is 12 rubles cheaper than the marker. We also know the total cost of the items is 658 rubles.

Solution

Let's assume the price of the pencil is x rubles.

According to the given information, the marker is 14 rubles more expensive than the pencil, so its price is x + 14 rubles.

The pen is 12 rubles cheaper than the marker, so its price is (x + 14) - 12 rubles.

Now, we can calculate the total cost of the items:

9 pens + 11 markers + 7 pencils = 658 rubles

Using the prices we calculated, we can write the equation:

9 * [(x + 14) - 12] + 11 * (x + 14) + 7 * x = 658

Simplifying the equation:

9x + 126 - 108 + 11x + 154 + 7x = 658

Combining like terms:

27x + 172 = 658

Subtracting 172 from both sides:

27x = 486

Dividing both sides by 27:

x = 18

Therefore, the price of the pencil is 18 rubles.

To find the price of the pen, we substitute the value of x into the equation:

Pen price = (x + 14) - 12 = (18 + 14) - 12 = 20 rubles.

Answer

The price of the pen is 20 rubles.

Explanation

Based on the given information, we can calculate the price of the pen by assuming the price of the pencil and using the relationships between the prices of the pen, marker, and pencil. By solving the equation, we find that the price of the pencil is 18 rubles and the price of the pen is 20 rubles.