Question

after her birthday, fiona had d dollars in gift money. she spent \\( \frac { 1 } { 3 } \\) of this on an electric skateboard. the next day, she spent \\( \frac { 1 } { 3 } \\) of what was left on a movie passcard, and then finally put the last \\( \\$ 80 \\) in the bank. if she made no other purchases with that money, then what was the value of d? choose the option that best answers the question. $240 $300 $320 $360

Explanation:

Step1: Calculate the amount of money left after buying the skateboard

She spent \(\frac{1}{3}\) of \(D\) on the skateboard, so the amount of money left is \(D-\frac{1}{3}D=\frac{2}{3}D\)

Step2: Calculate the amount of money after putting \(80\) in the bank

After putting \(80\) in the bank, the remaining money is \(\frac{2}{3}D - 80\)

Since this remaining money is \(0\) (because she made no other purchases), we set up the equation \(\frac{2}{3}D-80 = 0\)

Step3: Solve the equation for \(D\)

Add \(80\) to both sides of the equation: \(\frac{2}{3}D=80\)

Multiply both sides by \(\frac{3}{2}\): \(D = 80\times\frac{3}{2}=120\times2 = 360\)

Answer:

\(360\) (corresponding to the first option \(\$360\))