15. Jack has $$ k $$ dollars. He spend $$ \frac{3}{4} $$ of his money on a T-shirt and $$ \frac{1}{3} $$ of what was left on a sandwich. If this left him with $$ t $$ dollars, which of the following is the value of $$ k $$ in terms of $$ t $$ ? A. $$ 6 t $$ B. $$ 9 t $$ C. $$ 12 t $$ D. $$ 24 t $$

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UpStudy AI · Accepted Answer

Let $$ k $$ be the initial amount of money.

1. Jack spends $$\frac{3}{4}$$ of his money on a T-shirt. The remaining money after this purchase is:
   $$
   k - \frac{3}{4}k = \frac{1}{4}k.
   $$

2. He then spends $$\frac{1}{3}$$ of the remaining money on a sandwich. The amount spent on the sandwich is:
   $$
   \frac{1}{3} \times \frac{1}{4}k = \frac{k}{12}.
   $$

3. The money left after buying the sandwich is:
   $$
   \frac{1}{4}k - \frac{k}{12}.
   $$
   To subtract these fractions, find a common denominator:
   $$
   \frac{1}{4}k = \frac{3}{12}k.
   $$
   So,
   $$
   \frac{3}{12}k - \frac{k}{12} = \frac{2}{12}k = \frac{k}{6}.
   $$

4. According to the problem, the money left is $$ t $$ dollars:
   $$
   \frac{k}{6} = t.
   $$
   Solving for $$ k $$:
   $$
   k = 6t.
   $$

Thus, the value of $$ k $$ in terms of $$ t $$ is $$\boxed{6t}$$, which corresponds to option A.
$$ k = 6t $$

Jack has dollars. He spend of his
money on a T-shirt and of what was
left on a sandwich. If this left him with
dollars, which of the following is the
value of in terms of ?
A.
B.
C.
D.

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Jack has dollars. He spend of his money on a T-shirt and of what was left on a sandwich. If this left him with dollars, which of the following is the value of in terms of ? A. B. C. D.