One fourth times the difference of ten and a variable is two thirds.
one fourth times the quantity y minus 10 equals two thirds
one fourth times y minus 10 equals two thirds
one fourth times the quantity 10 minus y equals two thirds
one fourth times 10 minus y equals two thirds
The correct equation is:
"One fourth times the quantity y minus 10 equals two thirds."
This can be written as:
(1/4)(y - 10) = 2/3
The correct equation is: one fourth times the difference of ten and a variable is two thirds.
Mathematically, this can be written as:
1/4 * (10 - y) = 2/3
Where 'y' is the variable we are trying to find.
To determine the correct equation based on the given information, we need to interpret the problem statement. Let's break it down step by step:
The problem states the expression "one fourth times the difference of ten and a variable." This can be represented as 1/4 * (10 - y).
The problem also states that this expression is equal to two thirds. So, we set up the equation:
1/4 * (10 - y) = 2/3
Now, let's analyze the options you provided:
1. one fourth times the quantity y minus 10 equals two thirds: This is not the correct option as it doesn't match the original expression. It reverses the order of subtraction.
2. one fourth times y minus 10 equals two thirds: This option is incorrect because it doesn't correctly represent the "one fourth times" part of the problem. It only multiplies y by one-fourth instead of the entire expression.
3. one fourth times the quantity 10 minus y equals two thirds: This option is incorrect as it reverses the order of subtraction from the original expression.
4. one fourth times 10 minus y equals two thirds: This is the correct option as it matches the original expression: 1/4 * (10 - y) = 2/3.
Therefore, the correct equation based on the given information is:
one fourth times 10 minus y equals two thirds.