Question

The English Alphabet has 20 letters more than one-fourth the number of letters in the Greek Alphabet. The English Alphabet has 26 letters. Which of the following equations would you use to find the number of letters, g, in the Greek Alphabet?
Answer
1/4g + 20 = 26
4g - 26 = 20
4g - 20 = 26
g+20/4=26

Answer 1

we are given that the English Aplhabet has 26 letters. we let g represent the number of letters in the Greek alphabet. From the statement given, English alphabet which is 26 = 20 + 1/4 *g. The expression which is similar to this is in option A. 1/4g + 20 = 26

Answer 2

Let $e$ be the number of letters in the English alphabet, and let $g$ be the number of letters in the Greek Alphabet.

We know from our problem that the English alphabet has 20 letters more than one-fourth the number of letters in the Greek alphabet, so the number of English letters minus 20 will be equal to one-fourth the number of Greek letters -after all, the English alphabet has 20 letters more than one-fourth of the Greek's, so we need to subtract those 20 letters form the English alphabet to make it equal to one-fourth of the Greek alphabet.

Since $e$ is the number of letters in the English alphabet, and $g$ the number of letters in the Greek Alphabet, we can express our paragraph using those symbols:

$e-20=\frac{1}{4} g$

Now we can play with our equation to get the equation from the list that we should use to find the number of letters in the Greek alphabet.

Lets add 20 to both sides of the equation:

$e-20+20=\frac{1}{4} g+20$

$e=\frac{1}{4} g+20$

We know that the number of letters in the English alphabet is 26, so $e=26$:

$26=\frac{1}{4} g+20$

Now the only thing left is using the reflexive property: if $a=b$ then $b=a$, so $26=\frac{1}{4} g+20$ is the same as $\frac{1}{4} g+20=26$

We can conclude that the correct answer is: 1/4g + 20 = 26

Just for fun, lets solve our equation to find the number of letters in the Greek Alphabet:

$\frac{1}{4} g+20=26$

Step 1 subtract 20 from both sides of the equation:

$\frac{1}{4} g+20-20=26-20$

$\frac{1}{4} g=6$

Step 2 divide both sides of the equation by $\frac{1}{4}$:

$\frac{\frac{1}{4}g}{\frac{1}{4}} =\frac{6}{\frac{1}{4}}$

$g=24$

The Greek alphabet has 24 letters.