2014 CEMC Gauss (Grade 8) Problems/Problem 6

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

2014 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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2014 CEMC Gauss (Grade 8) Problems/Problem 6

Contents

Problem

Solution 1

Solution 2

Solution 3 (answer choices)