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Musya8 [376]
3 years ago
6

In a certain game, a player can solve easy or hard puzzles. A player earns 30 points for solving an easy puzzle and 60 points fo

r solving a hard puzzle. Tina solved a total of 50 puzzles playing this game, earning 1,950 points in all. How many hard puzzles did Tina solve?
Mathematics
1 answer:
Karolina [17]3 years ago
3 0

This is a system of equations. We can solve it by recognizing the two linear equalities we've given to solve this equation.

First, let's start off by recognizing two variables: x and y. x will be our number of hard puzzles, and y will be our number of easy puzzles. We're given that the number of hard puzzles and easy puzzles sum to 50, so we can rewrite that as:

x+y=50

Next, we're given that the sum of the points gained from the hard puzzles (60x), and the number of points gained from the easy puzzles (30y), sum to 1950. We can rewrite that as:

60x+30y=1950

Now, we have our two linear equations, and we must solve for the hard puzzles, so x. Solving for the hard puzzles means eliminating the easy puzzles from our systems, so we can multiply our first equation by 30, and subtract it from the first equation. This is a technique called elimination.

30x+30y=1500 \\ 60x+30y=1950 \\ 30x=450 \implies x=15

Since x=15, Tina has solved 15 hard puzzles.

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PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Tanya [424]

Answer:

NI = 45

IG=28

HG^2 = NI^2 +IG^2

= 45^2 +28^2

=2025+784

= 2809

HG=53

CosG = IG/HG

= 28/53

= 0.52

8 0
2 years ago
SOMEONE PLZ HELP ME ASAP
Marizza181 [45]

Answer:

XW = 4 units

Step-by-step explanation:

Given tanf° = \frac{2}{1}, then

tanf° = \frac{opposite}{adjacent} = \frac{YW}{XW} = \frac{8}{XW} = \frac{2}{1} ( cross- multiply )

2XW = 8 ( divide both sides by 2 )

XW = 4

4 0
3 years ago
3(x-1)=2x+5 what is the solution
ser-zykov [4K]
3(x-1)=2x+5
3x-3=2x+5
3x-2x=3+5
x=8
6 0
3 years ago
Read 2 more answers
If y varies with x, and y=-20 and x=5, what is x when y=-30?
vladimir1956 [14]

If y = -30, then x = 7.5

Hope this helps.

3 0
3 years ago
78 is what percent of 110
irinina [24]

Answer: 70.909090909091%

Step-by-step explanation: Reading through the problem we have <em>78 is</em>, that's 78 equals, <em>what percent</em>, x/100, <em>of 110</em>, times 110.

It's important to understand that <em>percent</em> means over 100 so what percent would simply mean <em>x/100</em> or any variable but I will be using x.

So we have the equation 78 = \frac{x}{100} *110

So cross canceling the 110 and 100 to 11 and 10, we have 78 = \frac{11x}{10}

Multiply both sides by 10 to get rid

of the fraction and we have 780 = 11x.

Now divide both sides by 11 and 70.909090909091 = x.

So, 78 is 70.909090909091% of 110.

Work is attached in the image provided.

8 0
3 years ago
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