
6. У Максима есть 30 монет: 1, 2, 5 и 10- ти рублевые. Среди этих моне двухрублёвые, 24 монеты —
не пятирублёвые, 23 монеты — не ОДНОрублевые Сколько десятирублёвых монет у Максима?

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Solving for the Number of Ten-Ruble Coins
To solve this problem, we can use a system of equations based on the given information.
Let's denote the number of one-ruble coins as x, the number of two-ruble coins as y, the number of five-ruble coins as z, and the number of ten-ruble coins as w.
We are given the following information: 1. Maxim has 30 coins in total: - This gives us the equation: x + y + z + w = 30.
2. There are two-ruble coins: - This gives us the equation: y > 0.
3. There are 24 coins that are not five-ruble coins: - This gives us the equation: x + y + w = 24.
4. There are 23 coins that are not one-ruble coins: - This gives us the equation: y + z + w = 23.
Let's solve for the number of ten-ruble coins, w.
First, we can simplify the equations to make them easier to work with.
From the equation x + y + z + w = 30, we can express x in terms of y, z, and w: x = 30 - y - z - w.
From the equation x + y + w = 24, we can express z in terms of y and w: z = 24 - x - y.
Now, we can substitute these expressions into the equation y + z + w = 23 to solve for w.
Solving the Equations
Let's start by substituting the expression for x into the equation x + y + w = 24: 30 - y - z - w + y + w = 24, 30 - z = 24, z = 30 - 24, z = 6.
Now, we can substitute the value of z into the equation y + z + w = 23: y + 6 + w = 23, y + w = 23 - 6, y + w = 17.
So, we have the equation y + w = 17.
Now, we know that y > 0, so the minimum value of y is 1. Therefore, the minimum value of w is 16.
Answer
Maxim has at least 16 ten-ruble coins.


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