PLEASE HELP!!!!!!!! WILL GIVE 10 POINTS!!!!!!!

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.

x + y = 24

3x + 5y = 100

What does the solution of this system indicate about the questions on the test?

The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions

Question

contestada

Respuesta :

absor201 absor201 · Answer 1 · 2019-11-28T16:27:06+01:00

The test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

Given equations are;

x + y = 24 Eqn 1

3x + 5y = 100 Eqn 2

Multiplying Eqn 1 by 3;

[tex]3(x+y=24)\\3x+3y=72\ \ \ Eqn 3\\[/tex]

Subtracting Eqn 3 from Eqn 2;

[tex](3x+5y)-(3x+3y)=100-72\\3x+5y-3x-3y=28\\2y=28[/tex]

Dividing both sides by 2;

[tex]\frac{2y}{2}=\frac{28}{2}\\y=14\\[/tex]

Putting in Eqn 1,

[tex]x+14=24\\x=24-14\\x=10[/tex]

The test contains 10 three-point questions and 14 five-point questions.

Keywords: linear equations, subtraction

Learn more about linear equations at:

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