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Answer :
Let's solve the problem step by step.
1. Define the variable:
Let's designate [tex]\( x \)[/tex] to represent the amount of the first bill in dollars.
2. Relate the second bill to the first bill:
According to the problem, the second bill was [tex]$5 more than twice the amount of the first bill. Therefore, the cost of the second bill can be expressed as:
\[
2x + 5
\]
where \( 2x \) is twice the amount of the first bill, and adding $[/tex]5 gives us the second bill's cost.
3. Set up the equation using the total cost:
The combined cost of the two bills is given to be [tex]$157. This means if we add the cost of the first bill (\( x \)) and the cost of the second bill (\( 2x + 5 \)), the total will equal $[/tex]157:
[tex]\[
x + (2x + 5) = 157
\][/tex]
4. Simplify the equation:
Combine like terms on the left side of the equation:
[tex]\[
x + 2x + 5 = 157
\][/tex]
[tex]\[
3x + 5 = 157
\][/tex]
5. Match the equation to the given choices:
The equation [tex]\( x + (2x + 5) = 157 \)[/tex] corresponds directly with option D:
[tex]\[
x + (2 x + 5) = 157
\][/tex]
Thus, the correct option is:
[tex]\[
\boxed{D}
\][/tex]
1. Define the variable:
Let's designate [tex]\( x \)[/tex] to represent the amount of the first bill in dollars.
2. Relate the second bill to the first bill:
According to the problem, the second bill was [tex]$5 more than twice the amount of the first bill. Therefore, the cost of the second bill can be expressed as:
\[
2x + 5
\]
where \( 2x \) is twice the amount of the first bill, and adding $[/tex]5 gives us the second bill's cost.
3. Set up the equation using the total cost:
The combined cost of the two bills is given to be [tex]$157. This means if we add the cost of the first bill (\( x \)) and the cost of the second bill (\( 2x + 5 \)), the total will equal $[/tex]157:
[tex]\[
x + (2x + 5) = 157
\][/tex]
4. Simplify the equation:
Combine like terms on the left side of the equation:
[tex]\[
x + 2x + 5 = 157
\][/tex]
[tex]\[
3x + 5 = 157
\][/tex]
5. Match the equation to the given choices:
The equation [tex]\( x + (2x + 5) = 157 \)[/tex] corresponds directly with option D:
[tex]\[
x + (2 x + 5) = 157
\][/tex]
Thus, the correct option is:
[tex]\[
\boxed{D}
\][/tex]
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