Question

В шести маленьких коробках и в двух больших коробках 40 карандашей.в одной маленькой коробке в 2 раза меньше карандашей,чем в большой. сколько карандашей в маленькой коробке и в большой ?

Answer 1

X-маленькая коробка
y-большая коробка
2x=y
6x+2y=40
6x+2(2x)=40
6x+4x=40
10x=40
x=40/10
x=4
2x=40-x
4-в маленькой коробке
y=4*2
y=8
8-в большой корбке

Answer 2

В 1большой.-----2x
В 1 мал.---x
6x+2*2x=40x
X=4 карандаша в мал.
2*4=8 каран. В больш.

Answer 3

Problem Analysis

We are given that there are 6 small boxes and 2 large boxes, and the total number of pencils in all the boxes is 40. It is also mentioned that the number of pencils in one small box is half the number of pencils in one large box. We need to find the number of pencils in each small box and each large box.

Solution

Let's assume the number of pencils in one small box is x and the number of pencils in one large box is y.

From the given information, we can form the following equations: 1. There are 6 small boxes, so the total number of pencils in the small boxes is 6 times the number of pencils in one small box: 6x. 2. There are 2 large boxes, so the total number of pencils in the large boxes is 2 times the number of pencils in one large box: 2y. 3. The total number of pencils in all the boxes is 40: 6x + 2y = 40. 4. The number of pencils in one small box is half the number of pencils in one large box: x = y/2.

We can solve these equations to find the values of x and y.

Solving the Equations

Let's substitute the value of x from equation 4 into equation 3: 6(y/2) + 2y = 40

Simplifying the equation: 3y + 2y = 40 5y = 40 y = 8

Now, substitute the value of y into equation 4 to find x: x = 8/2 x = 4

Answer

Therefore, there are 4 pencils in each small box and 8 pencils in each large box.

Verification

Let's verify our answer using the given information.

According to the problem statement, there are 6 small boxes and 2 large boxes. The number of pencils in each small box is half the number of pencils in each large box.

If we calculate the total number of pencils using our answer, we get: 6 small boxes * 4 pencils per small box = 24 pencils in small boxes 2 large boxes * 8 pencils per large box = 16 pencils in large boxes

The total number of pencils is 24 + 16 = 40, which matches the given information.

Therefore, our answer is verified.