Answered

1. Levi paid two bills. The cost of the two bills was [tex]\$ 157[/tex]. The second bill was [tex]\$ 5[/tex] more than twice the amount of the first bill. Which of the following equations could be used to find the amount of the first bill?

A. [tex]5 - 2x = 157[/tex]

B. [tex]2x - 5 = 157[/tex]

C. [tex]x - (2x + 5) = 157[/tex]

D. [tex]x + (2x + 5) = 157[/tex]



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]