In this article, we’re going to solve a math problem about MacDonald and his orange trees. The challenge is to figure out how many trees MacDonald originally had on his farm before he had to cut some down because of insect problems.
MacDonald had a certain number of orange trees, which we’ll call t. To deal with insects, he cut down 5 trees. After that, the remaining trees produced a total of 41,790 oranges, with each tree giving 210 oranges. Our task is to find out how many trees MacDonald started with.
After cutting down 5 trees, the number of trees left is t – 5. The total oranges from these trees can be written as:
(t – 5) × 210 = 41,790
This equation helps us find t, the initial number of trees.
First, we can simplify the equation by dividing both sides by 210:
t – 5 = 41,790 ÷ 210
Let’s do the division:
So, we find:
41,790 ÷ 210 = 199
Now, add 5 to both sides to find t:
t = 199 + 5 = 204
Another way is to distribute the 210 in the original equation:
210(t – 5) = 41,790
This expands to:
210t – 1,050 = 41,790
Adding 1,050 to both sides gives us:
210t = 42,840
Now, divide both sides by 210:
t = 42,840 ÷ 210
Doing the division again gives us the same result:
t = 204
After solving the problem using two different methods, we find that MacDonald initially had 204 orange trees on his farm. This exercise shows how important it is to set up equations correctly and how different methods can lead to the same answer.
Imagine you are MacDonald and create a simulation of the farm using small objects like coins or buttons to represent the trees. Start with 204 objects, then remove 5 to simulate the cutting down of trees. Count the remaining objects to ensure you have 199. This will help you visualize the problem and understand the subtraction involved.
Create a puzzle by writing the equation (t – 5) × 210 = 41,790 on a piece of paper. Cut the paper into pieces, each containing a part of the equation. Mix them up and challenge yourself to rearrange the pieces to form the correct equation. This activity will reinforce your understanding of how the equation is structured.
Work in pairs to solve the division 41,790 ÷ 210 as quickly as possible. Take turns performing each step of the division process, such as dividing, multiplying, and subtracting. This will help you practice long division and teamwork.
Write a short story or comic strip that explains the problem MacDonald faced with his trees. Include characters, dialogue, and illustrations to show how he solved the problem using the equation. This creative activity will help you understand the problem-solving process in a fun way.
Become a math detective and solve the problem using both methods described in the article: dividing both sides and distributing the 210. Compare your results and write a report on which method you found easier and why. This will help you analyze different problem-solving strategies.
Trees – In mathematics, a tree is a connected graph with no cycles, often used to represent hierarchical structures. – In our math class, we learned how to use trees to organize data in a structured way.
Oranges – In algebra, “oranges” can be used as a variable or placeholder in word problems to represent unknown quantities. – If you have 3 oranges and you buy 5 more, how many oranges do you have in total?
Equation – An equation is a mathematical statement that asserts the equality of two expressions. – To find the value of x, we need to solve the equation 2x + 3 = 11.
Divide – To divide means to separate a number into equal parts or groups. – When you divide 20 by 4, you get 5.
Method – A method is a systematic way of solving a problem or performing a task in mathematics. – The teacher showed us a new method to solve quadratic equations.
Initial – In mathematics, initial often refers to the starting value or condition in a problem. – The initial value of the sequence is 5, and each term increases by 3.
Solve – To solve means to find the answer to a problem or equation. – We need to solve for x in the equation x + 7 = 12.
Number – A number is a mathematical object used to count, measure, and label. – The number 8 is even, and it can be divided by 2 without a remainder.
Distribute – In algebra, distribute refers to the process of multiplying each term inside a parenthesis by a factor outside the parenthesis. – To simplify the expression, distribute the 3 across the terms inside the parentheses: 3(x + 4).
Subtract – To subtract means to take away one quantity from another. – When you subtract 5 from 10, you are left with 5.
