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? Use this to solve the problem.

Question

__ = 55; x = __ tangerines in each basket

Answer 1

To solve the problem, we need to set up an equation based on the information given:

Farah is making 5 baskets, and each basket contains:

• 1 cantaloupe
• 1 pineapple
• 1 mango

This means each basket has 3 pieces of fruit (1 of each type of fruit), and with 5 baskets, the total number of cantaloupes, pineapples, and mangoes is:

\[ 5 \text{ cantaloupes} + 5 \text{ pineapples} + 5 \text{ mangoes} = 15 \text{ pieces of fruit} \]

Now, Farah has 55 pieces of fruit in total. The rest of the fruits in the baskets will be tangerines. If we let \(x\) be the number of tangerines in each basket, then in total she will use \(5x\) tangerines.

Now, we can set up the equation:

\[ 15 + 5x = 55 \]

Next, we can solve for \(x\):

1. Subtract 15 from both sides: \[ 5x = 55 - 15 \] \[ 5x = 40 \]

2. Divide both sides by 5: \[ x = \frac{40}{5} \] \[ x = 8 \]

So, the equation representing this problem is:

\[ 15 + 5x = 55 \]

And after solving, we find that \(x = 8\). The meaning of \(x\) is that Farah will put 8 tangerines in each basket.