On a trivia game show, a contestent will answer 21 questions. A maximum of 200 points cana be earned. Some questions are worth 10 points and some are worth 8 points. Howmany of each point-value question must the contestent answer to earn the manimum number of points?
X 10-point questions.
Y 5-point questions.
Eq1: X + Y = 21 Questions
Eq2: 10x + 5y = 200 Points.
Multiply Eq1 by -5 and add Eq1 and Eq2:
-5x - 5y = -105
10x + 5y = 200
Solution set: (X,Y) = (19,2).
5x = 95
X = 19
In Eq1, replace x with 19:
19 + y = 21
Y = 2.
To solve this problem, we need to set up equations based on the given information. Let's assume the contestant answers x questions worth 10 points and y questions worth 8 points.
We know that a maximum of 200 points can be earned in total, so we can set up the first equation:
10x + 8y = 200
We also know that the contestant will answer a total of 21 questions, so we can set up the second equation:
x + y = 21
Now we have a system of two equations with two variables. We can solve it using either substitution or elimination method.
Let's solve it by substitution:
From the second equation, we can isolate x as x = 21 - y.
Now, substitute x in the first equation:
10(21 - y) + 8y = 200
Distribute 10 to the terms inside the parentheses:
210 - 10y + 8y = 200
Combine like terms:
-2y = -10
Divide both sides of the equation by -2:
y = 5
Now, substitute the value of y back into the second equation to find x:
x + 5 = 21
Subtract 5 from both sides of the equation:
x = 16
Therefore, the contestant needs to answer 16 questions worth 10 points and 5 questions worth 8 points to earn the minimum number of points.