Question

Решить задачу:В зрительном зале 80 больших и малых электрических лампочек.В течении вечера горение одной большой лампочки обходится в 13 тенге,а горение малой лампочки в 9 3/4 тенге.Сколько больших и сколько малых лампочек в зрительном зале,если овещение его в течение вечера обходится в 884 тенге?

Answer 1

Х - большая лампочка
у - маленькая лампочка

Решаем систему уравнений:
х+у=80
13х + 9 3\4у = 884

х = 80 - у
13 * (80 - у) + 9,75 у = 884
1040 - 13у + 9,75 у = 884
- 13у + 9,75 у = 884 - 1040
-3,25у = -156
у = 48 - маленькие лампочки
80 - 48 = 32 - большие лампочки

Answer 2

Problem Analysis

We are given the cost of burning one large lamp and one small lamp for an evening, as well as the total cost of lighting the auditorium for the evening. We need to determine the number of large and small lamps in the auditorium.

Solution

Let's assume that there are x large lamps and y small lamps in the auditorium.

The cost of burning one large lamp for an evening is 13 tenge, and the cost of burning one small lamp is 9 3/4 tenge.

The total cost of lighting the auditorium for the evening is given as 884 tenge.

We can set up the following equation to represent the total cost:

13x + (39/4)y = 884 To solve this equation, we can use the method of substitution or elimination.

Method of Substitution

We can solve the equation by solving one variable in terms of the other and substituting it back into the equation.

Let's solve the equation for x in terms of y:

13x = 884 - (39/4)y

x = (884 - (39/4)y)/13

Now, we can substitute this expression for x back into equation:

13((884 - (39/4)y)/13) + (39/4)y = 884

Simplifying the equation:

884 - (39/4)y + (39/4)y = 884

The (39/4)y terms cancel out, leaving us with:

884 = 884

This equation is true for any value of y. Therefore, there are infinitely many solutions to this problem.

We can choose any value for y and calculate the corresponding value for x using the equation x = (884 - (39/4)y)/13.

For example, if we choose y = 0, then x = (884 - (39/4)(0))/13 = 884/13 ≈ 68.

So, if there are 68 large lamps and 0 small lamps, the total cost of lighting the auditorium for the evening would be 884 tenge.

Similarly, we can choose other values for y and calculate the corresponding values for x.

Therefore, there are multiple possible combinations of large and small lamps that could be present in the auditorium.

Conclusion

The number of large and small lamps in the auditorium cannot be determined uniquely based on the given information. There are multiple possible combinations of large and small lamps that could result in a total cost of 884 tenge for lighting the auditorium for the evening.

Please let me know if I can help you with anything else.