The changes in the price of a certain stock each day from Monday to Thursday of one week were -$2.25, +$0.50, +$1.50, and +$0.75. If the overall change in the stock price for the week was -$0.50, write an equation that can be used to find the change in the price on Friday and explain two methods of solving this equation. Then solve the equation and explain its meaning in the context of the situation.
To find the change in the price on Friday, we can set up an equation that represents the overall change in the stock price for the week. Let's denote the change in the price on Friday as "x."
The equation can be written as:
(-$2.25) + (+$0.50) + (+$1.50) + (+$0.75) + x = -$0.50
Now let's explore two methods of solving this equation:
Method 1: Algebraic Approach
1. Combine the positive and negative values on the left side of the equation:
-$2.25 + $0.50 + $1.50 + $0.75 + x = -$0.50
2. Simplify the left side:
$0.50 + $1.50 + $0.75 + x = -$0.50 - (-$2.25)
$3.75 + x = -$0.50 + $2.25
$3.75 + x = $1.75
3. Isolate the variable:
x = $1.75 - $3.75
x = -$2.00
Method 2: Using Subtraction
1. Add up the changes from Monday to Thursday:
-$2.25 + $0.50 + $1.50 + $0.75 = $0.50
2. Subtract the sum from the overall change for the week:
x = -$0.50 - $0.50
x = -$1.00
The meaning of the solution, in the context of the situation, is that the stock price on Friday had a negative change of -$2.00 or -$1.00, depending on which method was used. This means the stock price decreased by either $2.00 or $1.00 on Friday, contributing to the overall change of -$0.50 for the week.