Question

Реши задачу составив систему уравнений для школы приобрели 15 хоккейных клюшек и 5 футбольных мячей уплатив за всю покупку 4650 р если бы купили 20 хоккейных клюшек и 15 футбольных мячей то уплатили бы 7450р сколько стоит клюшка и сколько стоит мяч

Answer 1

Х р. - стоит одна клюшка
у р. - стоит один мяч
15х+5у=4650
20х+15у=7450
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5(3х+у)=4650
20х+15у=7450
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3х+у=930
20х+15у=7450
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у=930-3х
20х+15у=7450
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у=930-3х
20х+15(930-3х)=7450
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у=930-3х
20х+13950-45х=7450
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у=930-3х
-25х=--6500
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у=930-3х
х=260
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у=930-3·260
х=260
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у=150
х=260
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Ответ: 260р.стоит одна клюшка, 150р. стоит один мяч.

Answer 2

Problem Analysis

To solve this problem, we need to find the individual prices of hockey sticks and footballs. We are given two scenarios: one where 15 hockey sticks and 5 footballs are purchased for a total of 4650 rubles, and another where 20 hockey sticks and 15 footballs are purchased for a total of 7450 rubles. We can set up a system of equations to represent these scenarios.

Let's assume the price of a hockey stick is x rubles and the price of a football is y rubles.

System of Equations

We can set up the following system of equations based on the given information:

Equation 1: 15x + 5y = 4650 Equation 2: 20x + 15y = 7450

Solving the System of Equations

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From Equation 1, we can express y in terms of x: 15x + 5y = 4650 5y = 4650 - 15x y = (4650 - 15x)/5 y = 930 - 3x

Now, substitute this expression for y in Equation 2: 20x + 15y = 7450 20x + 15(930 - 3x) = 7450 20x + 13950 - 45x = 7450 -25x + 13950 = 7450 -25x = 7450 - 13950 -25x = -6500 x = -6500 / -25 x = 260

Substitute the value of x back into Equation 1 to find y: 15x + 5y = 4650 15(260) + 5y = 4650 3900 + 5y = 4650 5y = 4650 - 3900 5y = 750 y = 750 / 5 y = 150

Solution

The price of a hockey stick is 260 rubles and the price of a football is 150 rubles.

Please note that the solution is based on the given information and the assumption that the prices of the hockey sticks and footballs remain constant.