Question

A farmer plants apple, pear, and cherry trees in an orchard. The number of apple trees is 8 more than twice the number of pear trees. The number of cherry and pear trees combined is 11 more than the number of apple trees. The farmer plants 143 trees total. How many of each type of tree did the farmer plant in the orchard?

1) 66 apple trees, 40 pear trees, and 37 cherry trees
2) 64 apple trees, 28 pear trees, and 50 cherry trees
3) 66 apple trees, 37 pear trees, and 40 cherry trees
4) 66 apple trees, 29 pear trees, and 48 cherry trees

Answer 1

The farmer planted 66 apple trees, 29 pear trees, and 48 cherry trees, which is the fourth option. By setting up equations based on the given information about the relationships between the numbers of each type of tree and solving the system, we can find the number of each type of tree the farmer planted.

Step-by-step explanation:

To solve the problem of how many apple, pear, and cherry trees the farmer planted, we need to set up a system of equations based on the information given:

• Let A represent the number of apple trees, P represent the number of pear trees, and C represent the number of cherry trees.
• The number of apple trees is 8 more than twice the number of pear trees: A = 2P + 8.
• The number of cherry and pear trees combined is 11 more than the number of apple trees: C + P = A + 11.
• The total number of trees is 143: A + P + C = 143.

Using these equations, we can solve for the number of each type of tree:

1. Substitute the expression for A from the first equation into the other two equations:
2. C + P = (2P + 8) + 11 => C + P = 2P + 19
3. (2P + 8) + P + C = 143
4. Simplify and solve the system of equations to get the values for P, C, and A.

After solving, we find the number of trees to be:

• 66 apple trees
• 29 pear trees
• 48 cherry trees

Hence, the correct answer is the fourth option: 66 apple trees, 29 pear trees, and 48 cherry trees.