The problem asks us to identify two cards from a given set of cards with mixed numbers such that the sum of the numbers on the two cards is equal to 5. The available cards are: $1 \frac{1}{4}$, $1 \frac{1}{2}$, $1 \frac{3}{4}$, $3 \frac{1}{2}$, $3 \frac{3}{4}$, and $4 \frac{1}{4}$.

1. Problem Description

The problem asks us to identify two cards from a given set of cards with mixed numbers such that the sum of the numbers on the two cards is equal to

5. The available cards are: $1 \frac{1}{4}$, $1 \frac{1}{2}$, $1 \frac{3}{4}$, $3 \frac{1}{2}$, $3 \frac{3}{4}$, and $4 \frac{1}{4}$.

2. Solution Steps

We need to find two mixed numbers from the given set that add up to

5. We can write each mixed number as an improper fraction to facilitate addition.

$1 \frac{1}{4} = \frac{5}{4}$

$1 \frac{1}{2} = \frac{3}{2} = \frac{6}{4}$

$1 \frac{3}{4} = \frac{7}{4}$

$3 \frac{1}{2} = \frac{7}{2} = \frac{14}{4}$

$3 \frac{3}{4} = \frac{15}{4}$

$4 \frac{1}{4} = \frac{17}{4}$

We are looking for two numbers that add up to 5, which is $\frac{20}{4}$.

We can try different combinations to see which sum is $\frac{20}{4} = 5$:

* $1\frac{1}{4} + 1\frac{1}{2} = \frac{5}{4} + \frac{6}{4} = \frac{11}{4} = 2\frac{3}{4}$

* $1\frac{1}{4} + 1\frac{3}{4} = \frac{5}{4} + \frac{7}{4} = \frac{12}{4} = 3$

* $1\frac{1}{4} + 3\frac{1}{2} = \frac{5}{4} + \frac{14}{4} = \frac{19}{4} = 4\frac{3}{4}$

* $1\frac{1}{4} + 3\frac{3}{4} = \frac{5}{4} + \frac{15}{4} = \frac{20}{4} = 5$

We found a pair that sums to 5: $1 \frac{1}{4}$ and $3 \frac{3}{4}$.

3. Final Answer

The two cards are $1 \frac{1}{4}$ and $3 \frac{3}{4}$.