1. (a) In the home for the elderly, they were celebrating the birthday of the oldest resident. They prepared 15 liters of a drink made from homemade pear juice, diluted with water, so that the drink contained $20\%$ water. As it was still too sweet, they added 5 liters of water. Calculate the percentage of natural juice in the resulting drink.

(b) In this home, they have a total of 141 rooms. 70 rooms are single rooms, the rest are double and triple rooms. If all rooms are fully occupied, there are 240 residents in the home. How many double and how many triple rooms do they have?

(10 points)
1. 

(a) In 15 liters of juice, 20% of 15 liters is 3 liters of water. Therefore, there are 12 liters of natural juice in 20 liters of the drink, which means the proportion of natural juice is 60%.

(b) We determine that the total number of double and triple rooms is 141 - 70 = 71. We write \( D + T = 71 \). Together, there are \( 2D + 3T = 170 \) residents in the double and triple rooms. Solving the system of equations, we get \( D = 43 \) and \( T = 28 \).

Calculation or determination that 3 liters of water are initially mixed in the juice ........................ 1 point

![](https://cdn.mathpix.com/cropped/2024_06_07_3b81dd7f2d1678befe89g-10.jpg?height=51&width=1725&top_left_y=1916&top_left_x=177)

![](https://cdn.mathpix.com/cropped/2024_06_07_3b81dd7f2d1678befe89g-10.jpg?height=54&width=1727&top_left_y=1966&top_left_x=176)

![](https://cdn.mathpix.com/cropped/2024_06_07_3b81dd7f2d1678befe89g-10.jpg?height=54&width=1727&top_left_y=2012&top_left_x=176)

We determine that the total number of double and triple rooms is \( 141 - 70 = 71 \)........ 1 point

The number of residents in double and triple rooms is 170 ................ 1 point

Writing the system of equations .................................................................................................................................................

Solving the system of equations ............................................................................................................

Answer .................................................................................................. 1 point

Note: If the student calculates that the drink contains 80% juice, they also get the point for the first part.