Question

in a certain game, a player can solve easy or hard puzzles. 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. How many hard puzzles did Tina solve

Answer 1

You use system of equations
30x+60y=1950
x+y=50

Isolate the x so, x=50-y
30(50-y)+60y=1950
1500-30y+60y=1950
1500+30y=1950
30y=450
y=15

Replace y with 15 in x+y=50
x+15=50
x=35

Then in order to confirm if these values are correct, you pluck them into the first equation, 30x+60y=1950
30(35)+60(15)=1950
1050+900=1950
1950=1950
Therefore proving the values true (:

Answer 2

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:

$x+y=50--------(1)\\30x+60y=1950---------(2)$

Multiply 60 in equation (1), we get

$60x+60y=3000-----(3)$

Subtract equation (2) from (3), we get

$30x=1050\\\\\Rightarrow\ x=\dfrac{1050}{30}=35$

Put x=-35 in (1), we get

$35+y=50\\\\\Rightarrow\ y=50-35=15$

Hence, Tine solved 15 hard puzzles.