Alan mixes 1 1/3

cups of milk with a can of condensed soup. He makes a total of 2 5/8
cups of soup. How many cups of condensed soup were in the can?

1 answer

To find out how many cups of condensed soup were in the can, we need to subtract the amount of milk from the total amount of soup.

  1. First, let's convert the mixed numbers into improper fractions.
  • For \(1 \frac{1}{3}\): \[ 1 \frac{1}{3} = \frac{4}{3} \]

  • For \(2 \frac{5}{8}\): \[ 2 \frac{5}{8} = \frac{16}{8} + \frac{5}{8} = \frac{21}{8} \]

  1. Now, we can set up the equation to find the amount of condensed soup (\(x\)): \[ x + \frac{4}{3} = \frac{21}{8} \]

  2. Solve for \(x\): \[ x = \frac{21}{8} - \frac{4}{3} \]

  3. To subtract these fractions, we need a common denominator. The least common multiple of \(8\) and \(3\) is \(24\).

    Convert the fractions:

    • Convert \(\frac{21}{8}\): \[ \frac{21}{8} = \frac{21 \times 3}{8 \times 3} = \frac{63}{24} \]
    • Convert \(\frac{4}{3}\): \[ \frac{4}{3} = \frac{4 \times 8}{3 \times 8} = \frac{32}{24} \]
  4. Now we can subtract: \[ x = \frac{63}{24} - \frac{32}{24} = \frac{31}{24} \]

  5. Convert \( \frac{31}{24} \) back to a mixed number: \[ \frac{31}{24} = 1 \frac{7}{24} \]

Thus, the amount of condensed soup in the can is \(\frac{31}{24}\) cups, or \(1 \frac{7}{24}\) cups.