1/4(90-x)+1/5(180-x)=36
multiply by 20
5(90-x) + 4(180-x) = 720
should be easy from here on
thank you. I was on the right track then :)
To solve the equation 1/4(90-x) + 1/5(180-x) = 36, we need to simplify the equation and solve for x.
First, let's simplify the equation by finding a common denominator for the two fractions. The common denominator for 4 and 5 is 20. We can rewrite the equation as follows:
(5/20)*(90-x) + (4/20)*(180-x) = 36
Next, we can distribute the numerators to the terms inside the parentheses:
(450/20 - (5/20)*x) + (720/20 - (4/20)*x) = 36
Now, we can simplify further by combining like terms:
(450/20 + 720/20) - (5/20)*x - (4/20)*x = 36
(1170/20) - (9/20)*x = 36
To isolate the x term, we can subtract (1170/20) from both sides:
- (9/20)*x = 36 - (1170/20)
Next, we can simplify the right side of the equation:
- (9/20)*x = (720/20) - (1170/20)
- (9/20)*x = -450/20
To eliminate the fraction, we can multiply both sides of the equation by the reciprocal of -(9/20), which is -(20/9):
x = -450/20 * -(20/9)
Now, we can simplify the expression by canceling out common factors:
x = 450/9
Finally, we can divide the numerator by the denominator to get the decimal approximation of x:
x ≈ 50
Therefore, the solution to the equation is x = 50.