The sum of two numbers is fourteen. Using x to represent the larger of the two numbers, translate "the difference between five more than the larger number and three times the smaller number" into a variable expression. Then simplify.
To translate "the difference between five more than the larger number and three times the smaller number" into a variable expression, let's break it down step by step.
1. The larger number is represented by x. So, "five more than the larger number" can be written as x + 5.
2. The smaller number can be represented by y. So, "three times the smaller number" can be written as 3y.
3. Finally, the "difference between five more than the larger number and three times the smaller number" can be written as (x + 5) - 3y.
Now, let's simplify this expression:
(x + 5) - 3y = x + 5 - 3y
So, the variable expression for "the difference between five more than the larger number and three times the smaller number" is x + 5 - 3y.
Let's break down the problem step by step:
Step 1: Assign variables
Let's assign x to represent the larger number and y to represent the smaller number.
Step 2: Set up the equation
Given that the sum of two numbers is fourteen, we can write the equation as:
x + y = 14
Step 3: Translate the problem into an expression
The "difference between five more than the larger number and three times the smaller number" can be represented as:
(5 + x) - (3 * y)
Step 4: Simplify
Simplifying the expression, we get:
5 + x - 3y
Therefore, the simplified variable expression representing the given problem is:
5 + x - 3y
x = larger
y = smaller
x + y = 14
y = 14 - x
5 more than the larger 5 + 14 -x
5 + 14-x - 3x
Now, simplify
19 -4x is the variable expression.