Mariana made strawberry jam and raspberry jam. She made enough strawberry jam to fill 2 1/2 jars. If she made 3 1/3 times as much raspberry jam as strawberry jam, how many jars will the raspberry jam fill?

Write your answer as a fraction or as a whole or mixed number.

jars

1 answer

To find out how many jars the raspberry jam will fill, we first need to calculate the amount of raspberry jam Mariana made in relation to the strawberry jam she prepared.

  1. We know that Mariana made enough strawberry jam to fill \(2 \frac{1}{2}\) jars. We can convert this mixed number to an improper fraction: \[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \] So, the amount of strawberry jam is \(\frac{5}{2}\) jars.

  2. Mariana made \(3 \frac{1}{3}\) times as much raspberry jam as strawberry jam. First, we convert \(3 \frac{1}{3}\) to an improper fraction: \[ 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \]

  3. Now, we calculate the amount of raspberry jam: \[ \text{Amount of raspberry jam} = \frac{10}{3} \times \text{Amount of strawberry jam} \] Substituting the amount of strawberry jam: \[ \text{Amount of raspberry jam} = \frac{10}{3} \times \frac{5}{2} \]

  4. We multiply the fractions: \[ \frac{10 \times 5}{3 \times 2} = \frac{50}{6} \]

  5. We simplify \(\frac{50}{6}\): \[ \frac{50 \div 2}{6 \div 2} = \frac{25}{3} \]

  6. Finally, we convert \(\frac{25}{3}\) to a mixed number: \[ \frac{25}{3} = 8 \frac{1}{3} \]

Thus, the raspberry jam will fill \(8 \frac{1}{3}\) jars.

The final answer is: \[ \boxed{8 \frac{1}{3}} \text{ jars} \]