Cara has a grocery bag with 13 total pieces of fruit. She can have pears, peaches, or a combination of pears and peaches in the bag. What combinations of fruit could be in the bag?

Question

Fill in some combinations of fruit that could be in the bag to have a total of 13 pieces of fruit.
Number of pears Number of peaches
5
6
12
13

Answer 1

To find the combinations of pears and peaches that sum to 13 pieces of fruit, we can represent the number of pears as \( p \) and the number of peaches as \( h \). The equation we need to satisfy is:

\[ p + h = 13 \]

We can calculate the number of peaches according to the number of pears given in your query. Here are the sets of combinations based on the number of pears:

1. If there are 5 pears (\( p = 5 \)): \[ h = 13 - 5 = 8 \quad \text{(Number of peaches = 8)} \] Combination: 5 pears and 8 peaches.

2. If there are 6 pears (\( p = 6 \)): \[ h = 13 - 6 = 7 \quad \text{(Number of peaches = 7)} \] Combination: 6 pears and 7 peaches.

3. If there are 12 pears (\( p = 12 \)): \[ h = 13 - 12 = 1 \quad \text{(Number of peaches = 1)} \] Combination: 12 pears and 1 peach.

4. If there are 13 pears (\( p = 13 \)): \[ h = 13 - 13 = 0 \quad \text{(Number of peaches = 0)} \] Combination: 13 pears and 0 peaches.

Summarizing the combinations:

| Number of Pears | Number of Peaches | |------------------|-------------------| | 5 | 8 | | 6 | 7 | | 12 | 1 | | 13 | 0 |

These are the possible combinations of pears and peaches that total 13 pieces of fruit.