Divide 75 units into 2parts,such that the product is 1,250.
50 + 25 = 75
x(75-x) = 1250
75 x - x^2 = 1250
x^2 - 75 x + 1250 = 0
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yes 50, 25 :)
To divide 75 units into two parts such that their product is 1,250, we can set up the following equation:
x * y = 1,250
Where x and y represent the two parts we are looking for.
Now, we need to find a pair of numbers whose product is 1,250 and whose sum is 75. One way to do this is by finding the prime factorization of 1,250, which is 2 * 5^4.
Let's try different combinations of factors to find the pair that adds up to 75. We can start by dividing 1,250 by 2:
1,250 ÷ 2 = 625
Since 625 is not a factor of 75, let's try the next prime factor, which is 5:
625 ÷ 5 = 125
Now we have a factor, 125, that we can divide by 5 again:
125 ÷ 5 = 25
Finally, we have another factor, 25, that we can divide by 5:
25 ÷ 5 = 5
By dividing 1,250 successively by its prime factors, we've found that the prime factorization of 1,250 is 2 * 5 * 5 * 5 * 5.
Now, we can rearrange these factors into pairs to find the parts that sum up to 75:
2 * (5 * 5 * 5) = 50 and (5 * 5) = 25
Therefore, the two parts that divide 75 units such that their product is 1,250 are 50 units and 25 units.