X is partly constant and partly varies as Y. X=15 when Y=3 and X=23 when Y=5. What is the value of X when Y=10?
X is partly constant and partly varies as Y ----> x = ky + c
X=15 when Y=3 ---> 15 = 3k + c
X=23 when Y=5 ---> 23 = 5k + c
subtracting them:
2k = 8
k = 4
put that back into 15 = 3k + c to find c
Now you have your complete equation and you can find x when y = 10
To find the value of X when Y=10, we can use the concept of proportionality.
Step 1: Determine the constant and variable parts of X in terms of Y.
Let's assume that X has a constant part, represented as k, and a variable part, represented as v. So, we have:
X = k + vY
Step 2: Use the given information to find the values of k and v.
Substituting the given values into the equation, we get two equations:
15 = k + 3v (when Y=3)
23 = k + 5v (when Y=5)
Now, we have a system of equations that we can solve.
Step 3: Solve the system of equations.
Subtracting the first equation from the second equation, we get:
23 - 15 = (k + 5v) - (k + 3v)
8 = 2v
Divide both sides of the equation by 2, we get:
v = 4
Substituting the value of v back into the first equation, we can solve for k:
15 = k + 3(4)
15 = k + 12
k = 15 - 12
k = 3
So, the constant part (k) is 3, and the variable part (v) is 4.
Step 4: Use the values of k and v to find the value of X when Y=10.
Using the equation X = k + vY, substitute the values of k, v, and Y:
X = 3 + 4(10)
X = 3 + 40
X = 43
Therefore, the value of X when Y=10 is 43.
To determine the value of X when Y=10, we need to understand how X varies with Y. From the given information, we know that X is partly constant and partly varies as Y.
Let's first determine the constant part of X. We are given that when Y=3, X=15. This represents the constant part of X.
Next, let's determine how X varies with Y. We are given that when Y=5, X=23. To find the variation, we can calculate the difference between the X values when Y changes by 1 unit. In this case, the difference between X values for Y=5 and Y=3 is 8 (23 - 15).
Since X varies as Y by a constant difference of 8, we can find the value of X when Y=10.
Starting with X=15 (when Y=3), we need to add the variation for every unit change in Y. Since the constant difference is 8, for every 1 unit increase in Y, X increases by 8.
To find X when Y=10, we need to calculate how many times Y increased by 1 unit from the initial value of 3 to reach 10.
Y increased by 1 unit 10-3 = 7 times.
Now, we can calculate the final value of X when Y=10:
X = Constant part + (Variation * Number of unit changes)
X = 15 + (8 * 7)
X = 15 + 56
X = 71
Therefore, when Y=10, the value of X is 71.