If 1/2 of a number is added to 1/5 of the same number, the results is 8. Find the number
1/2 + 1/5 = 7/10
So, you really have
7/10 x = 8
x = 8 * 10/7 = 80/7
check: 40/7 + 16/7 = 56/7 = 8
One-forth of a nber added to one-fith of the same number is less than or equal to 18. Find the range of values of the number
Let's assume the number is "x".
According to the information given, 1/2 of the number is x/2, and 1/5 of the same number is x/5.
So, the equation becomes:
x/2 + x/5 = 8
To solve this equation, we need to find a common denominator for the fractions. The common denominator for 2 and 5 is 10.
Multiplying every term by 10 to clear the fractions, we get:
5(x/2) + 2(x/5) = 8 * 10
Simplifying, we have:
5x/2 + 2x/5 = 80
Now, we can eliminate the fractions by multiplying every term by 10:
(10 * 5x)/2 + (10 * 2x)/5 = 80 * 10
Simplifying further:
25x + 4x = 800
Combining like terms:
29x = 800
Dividing both sides by 29 to solve for x:
x = 800/29
So, the number is approximately 27.5862
To find the number, let's set up an equation based on the given information.
Let's say the number is "x". According to the problem, "1/2 of the number is added to 1/5 of the same number, the result is 8". Mathematically, this can be written as:
1/2x + 1/5x = 8
Now, let's simplify the equation:
To add fractions, we need a common denominator. The least common denominator for 2 and 5 is 10.
So, let's rewrite the equation with the common denominator:
(5/10)x + (2/10)x = 8
Now, combine the terms with the same denominators:
(7/10)x = 8
To solve for x, we need to isolate it on one side of the equation. To do that, we'll multiply both sides of the equation by the reciprocal of the coefficient of x, which is 10/7:
(10/7)(7/10)x = (10/7)(8)
The multiplication cancels out the denominators:
x = 80/7
Therefore, the number is 80/7, which is approximately 11.43 when rounded to the nearest hundredth.