Question

В «Детском мире» продавали двухколёсные и трёхколёсные велосипеды. Миша пересчитал все рули и все колёса. Получилось 12 рулей и 27 колёс. Сколько трёхколёсных велосипедов продавали в «Детском мире»? Запиши решение и ответ. С пояснениями

Answer 1

2кол-x
3кол-y
{2x+3y=27
{x+y=12|×2
-{2x+3y=27
-{2x+2y=24
y=3
2x+3×3=27
2x=27-9
2x=18:2
x=9

Answer 2

Problem Analysis

Misha counted all the handlebars and wheels of bicycles sold in "Detkiy Mir" and found that there were 12 handlebars and 27 wheels. We need to determine how many three-wheeled bicycles were sold in "Detkiy Mir."

Solution

Let's assume that the number of two-wheeled bicycles sold is represented by x and the number of three-wheeled bicycles sold is represented by y.

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

1. The total number of handlebars is 12: 2x + 3y = 122. The total number of wheels is 27: 2x + 3y = 27 To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Multiply equation 1 by 3 and equation 2 by 2 to eliminate the y term:

3(2x + 3y) = 3(12) 2(2x + 3y) = 2(27)

Simplifying the equations:

6x + 9y = 36 4x + 6y = 54

Now, subtract equation 2 from equation 1:

(6x + 9y) - (4x + 6y) = 36 - 54 2x + 3y = -18

We have obtained a new equation:

2x + 3y = -18

Now, we can solve this equation for y:

3y = -18 - 2x y = (-18 - 2x) / 3

Since y represents the number of three-wheeled bicycles, it must be a whole number. We can substitute different values of x and check if y is a whole number.

Let's substitute x = 0:

y = (-18 - 2(0)) / 3 y = -18 / 3 y = -6

Since y is not a whole number, x = 0 is not a valid solution.

Let's substitute x = 1:

y = (-18 - 2(1)) / 3 y = (-18 - 2) / 3 y = -20 / 3

Since y is not a whole number, x = 1 is not a valid solution.

Let's substitute x = 2:

y = (-18 - 2(2)) / 3 y = (-18 - 4) / 3 y = -22 / 3

Since y is not a whole number, x = 2 is not a valid solution.

Let's substitute x = 3:

y = (-18 - 2(3)) / 3 y = (-18 - 6) / 3 y = -24 / 3 y = -8

Since y is not a whole number, x = 3 is not a valid solution.

Let's substitute x = 4:

y = (-18 - 2(4)) / 3 y = (-18 - 8) / 3 y = -26 / 3

Since y is not a whole number, x = 4 is not a valid solution.

Let's substitute x = 5:

y = (-18 - 2(5)) / 3 y = (-18 - 10) / 3 y = -28 / 3

Since y is not a whole number, x = 5 is not a valid solution.

Let's substitute x = 6:

y = (-18 - 2(6)) / 3 y = (-18 - 12) / 3 y = -30 / 3 y = -10

Since y is not a whole number, x = 6 is not a valid solution.

Let's substitute x = 7:

y = (-18 - 2(7)) / 3 y = (-18 - 14) / 3 y = -32 / 3

Since y is not a whole number, x = 7 is not a valid solution.

Let's substitute x = 8:

y = (-18 - 2(8)) / 3 y = (-18 - 16) / 3 y = -34 / 3

Since y is not a whole number, x = 8 is not a valid solution.

Let's substitute x = 9:

y = (-18 - 2(9)) / 3 y = (-18 - 18) / 3 y = -36 / 3 y = -12

Since y is not a whole number, x = 9 is not a valid solution.

Let's substitute x = 10:

y = (-18 - 2(10)) / 3 y = (-18 - 20) / 3 y = -38 / 3

Since y is not a whole number, x = 10 is not a valid solution.

Let's substitute x = 11:

y = (-18 - 2(11)) / 3 y = (-18 - 22) / 3 y = -40 / 3

Since y is not a whole number, x = 11 is not a valid solution.

Let's substitute x = 12:

y = (-18 - 2(12)) / 3 y = (-18 - 24) / 3 y = -42 / 3

Since y is not a whole number, x = 12 is not a valid solution.

Let's substitute x = 13:

y = (-18 - 2(13)) / 3 y = (-18 - 26) / 3 y = -44 / 3

Since y is not a whole number, x = 13 is not a valid solution.

Let's substitute x = 14:

y = (-18 - 2(14)) / 3 y = (-18 - 28) / 3 y = -46 / 3

Since y is not a whole number, x = 14 is not a valid solution.

Let's substitute x = 15:

y = (-18 - 2(15)) / 3 y = (-18 - 30) / 3 y = -48 / 3 y = -16

Since y is not a whole number, x = 15 is not a valid solution.

Let's substitute x = 16:

y = (-18 - 2(16)) / 3 y = (-18 - 32) / 3 y = -50 / 3

Since y is not a whole number, x = 16 is not a valid solution.

Let's substitute x = 17:

y = (-18 - 2(17)) / 3 y = (-18 - 34) / 3 y = -52 / 3

Since y is not a whole number, x = 17 is not a valid solution.

Let's substitute x = 18:

y = (-18 - 2(18)) / 3 y = (-18 - 36) / 3 y = -54 / 3 y = -18

Since y is not a whole number, x = 18 is not a valid solution.

Let's substitute x = 19:

y = (-18 - 2(19)) / 3 y = (-18 - 38) / 3 y = -56 / 3

Since y is not a whole number, x = 19 is not a valid solution.

Let's substitute x = 20:

y = (-18 - 2(20)) / 3 y = (-18 - 40) / 3 y = -58 / 3

Since y is not a whole number, x = 20 is not a valid solution.

From the above calculations, we can see that there are no valid whole number solutions for x and y. This means that there is no combination of two-wheeled and three-wheeled bicycles that satisfies the given conditions.

Therefore, we cannot determine the number of three-wheeled bicycles sold in "Detkiy Mir" based on the given information.

Answer

Based on the given information, we cannot determine the number of three-wheeled bicycles sold in "Detkiy Mir."