A college entry exam has 38 questions worth 200 points. The test consists of multiple-choice questions, 𝑥
x
, worth 4 points each and essay questions, 𝑦
y
, worth 10 points each.
is it
4𝑥+10𝑥=2004𝑦+10𝑦=38
4𝑥+10𝑦=384𝑥+10𝑦=14
4𝑥+10𝑦=38 𝑥+𝑦=200
or
4𝑥+10𝑦=200 𝑥+𝑦=38
this is the first time I've ever asked a question I have no idea how to do this please help, how do I do this math?
It says there are a total of 38 questions, x of which are multiple choice and y of which are essay type problems
or : x+y = 38
Now each of the x questions is worth 4 points, so you have 4x points
and each of the y questions is worth 10 points, so there are 10y points from there.
Is the total of those points not 200?
or 4x + 10y = 200
What matches that?
To solve this problem, we need to set up a system of equations based on the information given in the question. Let's break it down step by step:
Step 1: Define variables
Let's define the variables:
x = number of multiple-choice questions
y = number of essay questions
Step 2: Set up the equations
Based on the information given, we can set up two equations.
Equation 1: Points equation
The total points from the multiple-choice questions (4x) plus the total points from the essay questions (10y) should be equal to the total possible points on the exam (200).
So the equation becomes: 4x + 10y = 200
Equation 2: Questions equation
The total number of multiple-choice questions (x) plus the total number of essay questions (y) should be equal to the total number of questions on the exam (38).
So the equation becomes: x + y = 38
Now let's examine the options you provided and determine the correct equation:
Option 1: 4x + 10x = 200
This equation adds the total points from the multiple-choice questions (4x) to the total points from the essay questions (10x). However, this is incorrect because the number of essay questions should be represented by 'y' instead of 'x'. The correct equation should be 4x + 10y = 200.
Option 2: 4x + 10y = 384
This equation adds the total points from the multiple-choice questions (4x) to the total points from the essay questions (10y). However, the total points should be 200, not 384. Therefore, this option is incorrect.
Option 3: 4x + 10y = 38 and x + y = 200
This option is incorrect because the number of total questions (38) should be represented by 'x + y', and the total possible points (200) should be represented by '4x + 10y'.
Option 4: 4x + 10y = 200 and x + y = 38
This is the correct option. It correctly represents the equations based on the information given.
Therefore, the correct equations are:
4x + 10y = 200
x + y = 38
Now you can solve this system of equations to find the values of 'x' and 'y'. There are multiple methods to solve it, such as substitution or elimination.