if ` 1440 is divided into two parts in which one part is of the second, then 9 the smaller part is
The correct answer and explanation is:
Let the two parts be xx and yy, where xx is the smaller part and yy is the larger part. The problem states that 1440 is divided into two parts such that one part is the second part of the other, with a relation between the parts.
We are given that one part is 9 times the smaller part. So, the relationship between the parts is: y=9xy = 9x
Also, the sum of the two parts is 1440, so: x+y=1440x + y = 1440
Now, substitute the equation y=9xy = 9x into the sum equation: x+9x=1440x + 9x = 1440
Simplifying the equation: 10x=144010x = 1440
Solving for xx: x=144010=144x = \frac{1440}{10} = 144
Thus, the smaller part is x=144x = 144.
Now, substitute x=144x = 144 into the equation y=9xy = 9x to find the larger part: y=9×144=1296y = 9 \times 144 = 1296
So, the two parts are 144 and 1296. The smaller part is 144.
Explanation:
The total amount of 1440 is divided into two parts, with the larger part being 9 times the size of the smaller part. By setting up an equation with these conditions, we can easily solve for the smaller part. This is a simple problem involving linear equations and ratios, and the key to solving it lies in translating the problem into mathematical expressions and solving for the unknowns.