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Difference between revisions of "2014 CEMC Gauss (Grade 8) Problems/Problem 6"

(Created page with "==Problem== The value of <math>y</math> that satisfies the equation <math>5y - 100 = 125</math> is <math> \text{ (A) }\ 45\qquad\text{ (B) }\ 100\qquad\text{ (C) }\ 25\qqua...")
 
(I hate doing problems like this, but yea)
 
(One intermediate revision by the same user not shown)
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==Solution 1==
 
==Solution 1==
 
<math>5y - 100 = 125</math>
 
<math>5y - 100 = 125</math>
 +
 +
Adding <math>100</math> to both sides, we get:
  
 
<math>5y = 225</math>
 
<math>5y = 225</math>
Line 13: Line 15:
 
==Solution 2==
 
==Solution 2==
 
<math>5y - 100 = 125</math>
 
<math>5y - 100 = 125</math>
 +
 +
All of the terms as well as the [[coefficient]] of <math>y</math> is divisible by <math>5</math>. Dividing both sides by <math>5</math>, we get:
  
 
<math>y - 20 = 25</math>
 
<math>y - 20 = 25</math>
  
 
<math>y = \boxed {\textbf {(A) } 45}</math>
 
<math>y = \boxed {\textbf {(A) } 45}</math>
 +
 +
~anabel.disher
 +
==Solution 3 (answer choices)==
 +
We can notice that <math>5y - 100 = 125 > 0</math>. This means the answer for <math>y</math> cannot be less than <math>0</math>, eliminating choices D and E.
 +
 +
We can now try <math>45</math> since it is the median of the answer choices (excluding the eliminated choices) and then check whether or not the value found for <math>5y - 100</math> is too large, too small, or is correct. This gives:
 +
 +
<math>5 \times 45 - 100 = 225 - 100 = 125</math>
 +
 +
This is equal to <math>125</math>. Thus, the answer is <math>\boxed {\textbf {(A) } 45}</math>.
  
 
~anabel.disher
 
~anabel.disher

Latest revision as of 14:30, 29 April 2025

Problem

The value of $y$ that satisfies the equation $5y - 100 = 125$ is

$\text{ (A) }\ 45\qquad\text{ (B) }\ 100\qquad\text{ (C) }\ 25\qquad\text{ (D) }\ -25\qquad\text{ (E) }\ -5$

Solution 1

$5y - 100 = 125$

Adding $100$ to both sides, we get:

$5y = 225$

$y = \boxed {\textbf {(A) } 45}$

~anabel.disher

Solution 2

$5y - 100 = 125$

All of the terms as well as the coefficient of $y$ is divisible by $5$. Dividing both sides by $5$, we get:

$y - 20 = 25$

$y = \boxed {\textbf {(A) } 45}$

~anabel.disher

Solution 3 (answer choices)

We can notice that $5y - 100 = 125 > 0$. This means the answer for $y$ cannot be less than $0$, eliminating choices D and E.

We can now try $45$ since it is the median of the answer choices (excluding the eliminated choices) and then check whether or not the value found for $5y - 100$ is too large, too small, or is correct. This gives:

$5 \times 45 - 100 = 225 - 100 = 125$

This is equal to $125$. Thus, the answer is $\boxed {\textbf {(A) } 45}$.

~anabel.disher

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