There are 20 apple trees in the orchard. Each tree gives the same number of apples, and the barn already has 120 apples. After harvesting, the barn has 520 apples. How many apples are from each tree?
Mathia determined that in order to solve the equation, 20x + 120 = 520, she should use multiplication and then subtraction. Did she identify the correct operations?
Yes, Mathia correctly identified the operations to solve the equation.
Yes, Mathia correctly identified the operations to use in order to solve the equation. Let's break down the equation to understand why.
The equation, 20x + 120 = 520, represents the total number of apples in the barn.
The variable "x" represents the number of apples from each tree. Since there are 20 apple trees, multiplying "x" by 20 gives us the total number of apples from all the trees combined (20x).
The equation also states that the barn already had 120 apples before harvesting, so we add 120 to the total number of apples from the trees (20x + 120).
Finally, the equation states that after harvesting, the barn has 520 apples. Therefore, the total number of apples in the barn is equal to 520 (20x + 120 = 520).
To find the value of "x" (the number of apples from each tree), we need to isolate it on one side of the equation. Mathia correctly identified that we can achieve this by using the operations of multiplication and subtraction.
First, she multiplied 20 by "x" to get 20x. Then, she added 120 to 20x to get 20x + 120.
Next, to isolate "x", she subtracted 120 from both sides of the equation: 20x + 120 - 120 = 520 - 120.
Simplifying, we have 20x = 400.
Finally, Mathia divided both sides of the equation by 20 to solve for "x": 20x/20 = 400/20.
Therefore, Mathia's approach to solving the equation using multiplication and subtraction was correct.