Sure, let's solve this step-by-step.
Given the problem:
- Maria consumed [tex]\(\frac{1}{3}\)[/tex] of a liter.
- Jose consumed [tex]\(\frac{3}{4}\)[/tex] of a liter.
First, let's determine the total amount of coffee consumed by Maria and Jose. To do this, we need to add their individual consumptions together.
1. Maria's consumption:
[tex]\[
\frac{1}{3} \text{ liter}
\][/tex]
2. Jose's consumption:
[tex]\[
\frac{3}{4} \text{ liter}
\][/tex]
To add these fractions, we need to find a common denominator. The denominators are 3 and 4. The least common multiple (LCM) of 3 and 4 is 12.
Let's convert both fractions to have a denominator of 12:
- For Maria:
[tex]\[
\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
\][/tex]
- For Jose:
[tex]\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\][/tex]
Now, add these fractions:
[tex]\[
\frac{4}{12} + \frac{9}{12} = \frac{4 + 9}{12} = \frac{13}{12}
\][/tex]
So, the total amount of coffee consumed by Maria and Jose is [tex]\(\frac{13}{12}\)[/tex] liters.
Next, let's determine if there is any coffee remaining.
Since [tex]\(\frac{13}{12}\)[/tex] is greater than 1, this implies that Maria and Jose have consumed more than one liter of coffee combined.
To find the exact amount of coffee remaining, we subtract the total consumption from 1 liter:
[tex]\[
1 - \frac{13}{12} = \frac{12}{12} - \frac{13}{12} = \frac{12 - 13}{12} = -\frac{1}{12}
\][/tex]
Thus, the remaining amount of coffee is [tex]\(-\frac{1}{12}\)[/tex] liters, which means they have consumed [tex]\(\frac{1}{12}\)[/tex] liters more than what was available.
To summarize:
- Maria consumed approximately 0.333 liters.
- Jose consumed approximately 0.75 liters.
- They consumed 0.083 liters more than the initial 1 liter available.
