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Farah is making 5 fruit baskets as gifts for her family members. She has 55 total pieces of fruit to distribute among the baskets. She puts 1 cantaloupe, 1 pineapple, and 1 mango in each basket. She also has tangerines to put in each basket. What is the equation representing this problem, an what is the meaning of x once this equation is solved?

1 answer

To create the fruit baskets, Farah puts a fixed number of fruits in each basket. Let's summarize the fruit distribution:

  1. Each basket contains:
    • 1 cantaloupe
    • 1 pineapple
    • 1 mango
    • Some tangerines (let's denote the number of tangerines in each basket as \( x \))

Since there are 5 baskets, we can set up the equation based on the total number of fruits:

  1. Each basket contains 3 fruits (1 cantaloupe + 1 pineapple + 1 mango).

  2. For 5 baskets, the total number of these fruits is: \[ 5 \text{ baskets} \times 3 \text{ fruits per basket} = 15 \text{ fruits} \]

  3. Now, let’s denote the number of tangerines in each basket as \( x \). Therefore, the total number of tangerines in all the baskets is: \[ 5x \]

Combining these, the total number of fruits in the baskets is the fixed fruits plus the tangerines: \[ 15 + 5x = 55 \]

Now, we can rearrange this equation to solve for \( x \): \[ 5x = 55 - 15 \] \[ 5x = 40 \] \[ x = \frac{40}{5} \] \[ x = 8 \]

Conclusion:

The equation representing the problem is \( 15 + 5x = 55 \).

The meaning of \( x \), once this equation is solved, is the number of tangerines that Farah puts in each basket. In this case, \( x = 8 \), which means she puts 8 tangerines in each basket.