Answer:
$100
Step-by-step explanation:
Given information:
- $54 = cost of ticket
- Cost of hotel = 1/2 remaining money after purchase of ticket
- $7.90 = cost of food
- $15.10 = remaining money
Let x = money taken from bank account
If Sally paid $54 for her ticket, then the money remaining at that point can be defined as: [tex]x-54[/tex]
If the cost of the hotel was half of the remaining money, then:
[tex]\textsf{Cost of hotel}=\dfrac{1}{2}(x-54)}[/tex]
To find how much money Sally took from her bank account, create an equation with the given information and solve for x.
[tex]\implies \textsf{Money in bank} - \textsf{ticket} - \textsf{hotel} - \textsf{ food} =\textsf{remaining money}[/tex]
[tex]\implies x - 54 - \dfrac{1}{2}(x - 54)-7.90=15.10[/tex]
[tex]\implies x - 54 - \dfrac{1}{2}x+27-7.90=15.10[/tex]
[tex]\implies \dfrac{1}{2}x-34.90=15.10[/tex]
[tex]\implies \dfrac{1}{2}x=50[/tex]
[tex]\implies x=100[/tex]
Therefore, Sally took $100 from her bank account.
