Question

За три тетради и пять карандашей заплачено 7 р., а за пять таких же тетрадей и восемь карандашей заплачено 11р. 50 коп. Сколько стоила одна тетрадь и один карандаш?

Answer 1

За три тетради и пять карандашей заплачено 7 р., а за пять таких же тетрадей и восемь карандашей заплачено 11р. 50 коп. Сколько стоила одна тетрадь и один карандаш? 3x+5y=7 5x+8y=11,5 5y=7-3x y=1,4-0,6x 5x+11,2-4,8x=11,5 0,2x= 0,3 x=1,5 стоит тетрадь, y=1,4-0,6*1,5 у=0,5 стоит карандаш

Answer 2

Надо решить систему из 2 уравнений 3т+5к=7 и 5т+8к=11.5 отсюда карандаш стоит 50 копеек, а тетрадь 1,5 рубля

Answer 3

Problem Analysis

To solve this problem, we need to find the cost of one notebook and one pencil. We are given two equations:

Equation 1: 3 notebooks + 5 pencils = 7 rubles Equation 2: 5 notebooks + 8 pencils = 11 rubles 50 kopeks

We can solve these equations simultaneously to find the cost of one notebook and one pencil.

Solution

Let's solve the equations step by step.

Equation 1: 3 notebooks + 5 pencils = 7 rubles Equation 2: 5 notebooks + 8 pencils = 11 rubles 50 kopeks

To eliminate the variable "notebooks," we can multiply Equation 1 by 5 and Equation 2 by 3:

Equation 1 (multiplied by 5): 15 notebooks + 25 pencils = 35 rubles Equation 2 (multiplied by 3): 15 notebooks + 24 pencils = 34 rubles 50 kopeks

Now, subtract Equation 2 from Equation 1:

(15 notebooks + 25 pencils) - (15 notebooks + 24 pencils) = 35 rubles - (34 rubles 50 kopeks)

Simplifying the equation:

15 notebooks - 15 notebooks + 25 pencils - 24 pencils = 35 rubles - 34 rubles 50 kopeks

Pencils cancel out, and we are left with:

1 pencil = 50 kopeks

Now, substitute the value of one pencil into Equation 1:

3 notebooks + 5 pencils = 7 rubles

3 notebooks + 5 * 50 kopeks = 7 rubles

3 notebooks + 250 kopeks = 7 rubles

To convert kopeks to rubles, divide by 100:

3 notebooks + 2.50 rubles = 7 rubles

Subtract 2.50 rubles from both sides:

3 notebooks = 7 rubles - 2.50 rubles

3 notebooks = 4.50 rubles

Divide both sides by 3:

1 notebook = 4.50 rubles / 3

1 notebook = 1.50 rubles

Therefore, one notebook costs 1.50 rubles and one pencil costs 50 kopeks.

Conclusion

Based on the given information, one notebook costs 1.50 rubles and one pencil costs 50 kopeks.