B1. Three friends decided to buy healthy products instead of candy at the same store. The first one bought $0.5 \mathrm{~kg}$ of grapes, 30 dag of bananas, and 25 dag of apples and paid 2.20 euros. The second one bought 45 dag of bananas, 300 g of apples, and 25 dag of grapes and paid 1.98 euros. The third one bought $350 \mathrm{~g}$ of bananas, 20 dag of apples, and 30 dag of grapes and paid 1.74 euros. Calculate how much one kilogram of apples, one kilogram of grapes, and one kilogram of bananas cost.
B1. Let bananas be denoted by $x$, apples by $y$, and grapes by $z$. Convert all units to kilograms and set up a system of equations, for example: the first equation $0.30 x + 0.25 y + 0.50 z = 2.20$, the second equation $0.45 x + 0.30 y + 0.25 z = 1.98$, and the third equation $0.35 x + 0.20 y + 0.30 z = 1.74$. Solve the system of equations using any method, for example: multiply the equations by 100 and express $z$ from the first equation to get $z = \frac{220 - 30 x - 25 y}{50}$, substitute it into the second and third equations, simplify the equations, and obtain a system of two equations, for example: $60 x + 35 y = 176$ and $17 x + 5 y = 42$. Express $y$ from the second equation, for example: $y = \frac{42 - 17 x}{5}$, and substitute it into the first equation. We get the solutions to the equation $x = 2$, $y = 1.6$, and $z = 2.4$. Answer: One kilogram of bananas costs 2.00 euros, apples 1.60 euros, and grapes 2.40 euros.

![](https://cdn.mathpix.com/cropped/2024_06_07_9fbd0ae098c18b73b6bfg-19.jpg?height=51&width=1739&top_left_y=1228&top_left_x=176)

Equation $0.30 x + 0.25 y + 0.50 z = 2.20 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

Equation $0.45 x + 0.30 y + 0.25 z = 1.98 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

Equation $0.35 x + 0.20 y + 0.30 z = 1.74 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

![](https://cdn.mathpix.com/cropped/2024_06_07_9fbd0ae098c18b73b6bfg-19.jpg?height=54&width=1727&top_left_y=1429&top_left_x=176)

![](https://cdn.mathpix.com/cropped/2024_06_07_9fbd0ae098c18b73b6bfg-19.jpg?height=52&width=1727&top_left_y=1479&top_left_x=176)

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