If a certain number is increased by 5, one - half of the result is three - fifths of the excess of 61 over the number. Find the number
(n + 5) / 2 = 3/5 (61 - n)
5n + 25 = 366 - 6n
31
31
31
1/5(x+5)=3/5(61-x)
5(x+5)=6(61-x)
5x+25=366-6x
5x+6x=366-25
11x=341
x=31
To find the number, we first need to set up an equation based on the given information. Let's break down the question step by step:
1. "If a certain number is increased by 5" - let's call the number "x". So, the first part of the equation is "x + 5".
2. "One-half of the result is three-fifths of the excess of 61 over the number" - this means we need to find the difference between 61 and the number, multiply it by 3/5, and then set it equal to half of (x+5). In equation form, it is (61 - x) * (3/5) = (x+5) / 2.
Now, we solve this equation to find the value of "x".
Multiply both sides of the equation by 10 to eliminate the fractions:
10 * [(61 - x) * (3/5)] = 10 * [(x+5) / 2]
6 * (61 - x) = 5 * (x + 5)
Distribute and simplify:
366 - 6x = 5x + 25
Move all the "x" terms to one side and the constant terms to the other side:
366 - 25 = 5x + 6x
341 = 11x
Divide by 11 to solve for "x":
x = 341 / 11
x = 31
Therefore, the number is 31.