Answer: Tine solved 15 hard puzzles.
Step-by-step explanation:
Let x be the number of easy puzzles and y be the number of hard puzzels.
Given : A player earns 30 points for solving an easy puzzles and 60 points for solving a hard puzzled.
Tina solved a total of 50 Puzzles playing this game, earning 1950 points in all.
Then system of equations for above description:
[tex]x+y=50--------(1)\\30x+60y=1950---------(2)[/tex]
Multiply 60 in equation (1), we get
[tex]60x+60y=3000-----(3)[/tex]
Subtract equation (2) from (3), we get
[tex]30x=1050\\\\\Rightarrow\ x=\dfrac{1050}{30}=35[/tex]
Put x=-35 in (1), we get
[tex]35+y=50\\\\\Rightarrow\ y=50-35=15[/tex]
Hence, Tine solved 15 hard puzzles.
Using a system of equations, it is found that Tina solved 35 easy puzzles and 15 hard puzzles.
For our system, we are going to say that:
Total of 50 puzzles, thus:
[tex]x + y = 50[/tex]
Each easy puzzle earns 30 points, each hard 60, total of 1950 points, thus:
[tex]30x + 60y = 1950[/tex]
From the first equation:
[tex]x = 50 - y[/tex]
Replacing in the second:
[tex]30x + 60y = 1950[/tex]
[tex]30(50 - y) + 60y = 1950[/tex]
[tex]30y = 450[/tex]
[tex]y = \frac{450}{30}[/tex]
[tex]y = 15[/tex]
Then:
[tex]x = 50 - y = 50 - 15 = 35[/tex]
Tina solved 35 easy puzzles and 15 hard puzzles.
A similar problem is given at https://brainly.com/question/17096268
