Mr. Khater and Mr. Beck are both into collecting comics. Mr. Beck has 4 more than 3 times as many comics as Mr. Khater. Together they have 36 comics. Create a system of equations to represent the scenario above and use a model. How many more comics does Mr. Beck have than Mr Khater
Let's represent the number of comics Mr. Khater has as "K" and the number of comics Mr. Beck has as "B".
From the given information, we have the following two equations:
1) "Mr. Beck has 4 more than 3 times as many comics as Mr. Khater":
B = 3K + 4
2) "Together they have 36 comics":
B + K = 36
To find how many more comics Mr. Beck has than Mr. Khater, we need to subtract the number of comics Mr. Khater has from the number of comics Mr. Beck has:
B - K
Substituting the value of B from equation 1 into equation 2:
(3K + 4) - K = 36
Simplifying:
2K + 4 = 36
Subtracting 4 from both sides:
2K = 32
Dividing both sides by 2:
K = 16
Now we can substitute the value of K back into equation 1 to solve for B:
B = 3K + 4
B = 3(16) + 4
B = 48 + 4
B = 52
Therefore, Mr. Beck has 52 comics and Mr. Khater has 16 comics. To find how many more comics Mr. Beck has than Mr. Khater, we can subtract the number of comics Mr. Khater has from the number of comics Mr. Beck has:
52 - 16 = 36
So, Mr. Beck has 36 more comics than Mr. Khater.