Question

Один карандаш и четыре ручки стоят 1110 р., а четыре ручки и четыре карандаша 1440 р. Сколько стоят одна ручка и один карандаш?

Answer 1

1440-1110=330 р. стоит один карандаш и одна ручка

Answer 2

Problem Analysis

We are given the information that one pencil and four pens cost 1110 rubles, and four pens and four pencils cost 1440 rubles. We need to find the cost of one pen and one pencil.

Solution

Let's assume the cost of one pencil is x rubles and the cost of one pen is y rubles.

From the given information, we can form the following equations:

Equation 1: x + 4y = 1110 (one pencil and four pens cost 1110 rubles)

Equation 2: 4x + 4y = 1440 (four pencils and four pens cost 1440 rubles)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.

Multiplying Equation 1 by 4, we get:

4x + 16y = 4440 (Equation 3)

Subtracting Equation 2 from Equation 3, we get:

(4x + 16y) - (4x + 4y) = 4440 - 1440

Simplifying, we have:

12y = 3000

Dividing both sides by 12, we find:

y = 250

Substituting the value of y into Equation 1, we have:

x + 4(250) = 1110

Simplifying, we get:

x + 1000 = 1110

Subtracting 1000 from both sides, we find:

x = 110

Therefore, one pen costs 250 rubles and one pencil costs 110 rubles.

Answer

One pen and one pencil cost 250 rubles and 110 rubles, respectively.