Question

В 5 маленьких и 2 больших коробках 54 карандаша. в 3 маленьких и 2 больших 42 карандаша. сколько карандашей в одной маленькой и в одной большой коробке?

Answer 1

Х- карандашей в маленькой коробке
у- карандашей в большой коробке , из условия задачи имеем:
      5х + 2у =54
  {
      3х +2у =42     От первого уравнения отнимем второе , получим : 2х = 12    х =6 -карандашей в маленькой коробке , подставляя полученное во второе уравнение получим : 18 + 2у =42       2у = 24       у = 12 - карандашей в большой коробке

Answer 2

Calculating the Number of Pencils in Each Small and Large Box

To calculate the number of pencils in each small and large box, we can use the given information about the total number of pencils in 5 small and 2 large boxes, as well as the total number of pencils in 3 small and 2 large boxes.

Let's denote: - S: the number of pencils in a small box - L: the number of pencils in a large box

We are given the following information: - 5 small and 2 large boxes contain 54 pencils. - 3 small and 2 large boxes contain 42 pencils.

We can set up the following system of equations to solve for the number of pencils in each small and large box: 1. 5S + 2L = 54 2. 3S + 2L = 42

We can solve this system of equations to find the values of S and L.

Solving the System of Equations

Using the given information, we can solve the system of equations to find the number of pencils in each small and large box.

First, we can subtract equation 2 from equation 1 to eliminate L: 5S + 2L - (3S + 2L) = 54 - 42 2S = 12 S = 6

Now that we have the value of S, we can substitute it back into equation 1 to solve for L: 5(6) + 2L = 54 30 + 2L = 54 2L = 54 - 30 2L = 24 L = 12

Conclusion

Therefore, based on the given information, there are 6 pencils in each small box and 12 pencils in each large box.