Let's solve the problem step-by-step.
Step 1: Define the Variables
Let [tex]\( x \)[/tex] represent the amount of money that Sergi has.
Step 2: Express Avi’s Amount in Terms of Sergi’s
Avi has [tex]$2 more than double the amount of money Sergi has. Therefore, Avi's money can be represented as:
\[ 2x + 2 \]
Step 3: Set Up the Equation
Together, they have \$[/tex]40, so we sum up their amounts:
[tex]\[ x + (2x + 2) = 40 \][/tex]
Step 4: Simplify the Equation
Combine like terms:
[tex]\[ x + 2x + 2 = 40 \][/tex]
[tex]\[ 3x + 2 = 40 \][/tex]
Step 5: Solve for [tex]\( x \)[/tex]
First, subtract 2 from both sides of the equation to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[ 3x = 38 \][/tex]
Next, divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{38}{3} \][/tex]
[tex]\[ x \approx 12.67 \][/tex]
So, Sergi has approximately \[tex]$12.67.
Step 6: Calculate Avi’s Amount
Now that we know \( x \), we can find how much money Avi has:
\[ \text{Avi's amount} = 2x + 2 \]
\[ \text{Avi's amount} = 2 \left(\frac{38}{3}\right) + 2 \]
\[ \text{Avi's amount} \approx 25.33 + 2 \]
\[ \text{Avi's amount} \approx 27.33 \]
Therefore, Avi has approximately \$[/tex]27.33.
Step 7: Verify the Total
Finally, we verify their combined amount:
[tex]\[ \text{Total} = 12.67 + 27.33 = 40 \][/tex]
Thus, our calculations are consistent and correct.
The equation that determines how much money Sergi and Avi have together is:
[tex]\[ x + 2x + 2 = 40 \][/tex]
From the given options, the correct equation is:
[tex]\[ x + 2x + 2 = 40 \][/tex]
