If 5x and 9y =28 and x and y are positive integers what is the value of x?
I interpret 5x and 9y =28 as
5x + 9y = 25
since x and y must be positive integers,
5x could only have values of 5, 10, 15, 20, 25
9y could only have values of 9, 18, 27
now what number from the first set added to a number of the second set yields a sum of 28 ?
10 and 18
So x=2?
clearly, yes
To find the value of x, we need to solve the equation 5x + 9y = 28 given that x and y are positive integers.
Here's a step-by-step approach to solve the equation:
1. Start by substituting the value of y with its corresponding expression from the equation: 5x + 9y = 28.
We get: 5x + 9(28 - 5x) = 28.
2. Simplify the equation by expanding the brackets and combining like terms:
5x + 252 - 45x = 28.
Simplifying further, we get: -40x + 252 = 28.
3. Move the constant term to the other side of the equation by subtracting 252 from both sides:
-40x = 28 - 252.
Simplifying further, we get: -40x = -224.
4. Solve for x by dividing both sides of the equation by -40:
x = -224 / -40.
Simplifying further, we get: x = 5.6.
However, since x needs to be a positive integer, we round down the decimal value to the nearest whole number.
Hence, the value of x is 5.