A is partly constant and partly varies with B. When B =5, A=19 and when B=10, A=34. Find A when B is 7
A = k + mb
so, using the given data, you know that you just have to solve
k+5m = 19
k+10m=34
Clearly, m=3, so when B=7,
A = k+7m = k+5m + 2m = 19+6 = 25
To solve this problem, we can use a linear equation to represent the relationship between A and B. A linear equation is in the form of y = mx + b, where m is the slope and b is the y-intercept.
Given that A is partly constant and partly varies with B, we can write:
A = mB + b
We need to find the values of m and b. We are given two points: (5, 19) and (10, 34). We can use these points to form two equations:
Equation 1: A = mB + b (using point (5, 19))
Equation 2: A = mB + b (using point (10, 34))
Substituting the coordinates into the equations, we get:
Equation 1: 19 = 5m + b
Equation 2: 34 = 10m + b
Now we have a system of two equations with two variables (m and b). We can solve this system of equations to find the values of m and b.
Subtracting equation 1 from equation 2, we eliminate b:
34 - 19 = (10m + b) - (5m + b)
15 = 10m - 5m
15 = 5m
Dividing both sides by 5, we get:
m = 3
Now substitute the value of m into either equation 1 or equation 2 to solve for b. Let's use equation 1:
19 = 5m + b
19 = 5(3) + b
19 = 15 + b
Subtracting 15 from both sides, we get:
4 = b
Now we have the values of both m and b. The equation representing the relationship between A and B is:
A = 3B + 4
To find A when B is 7, substitute B = 7 into the equation:
A = 3(7) + 4
A = 21 + 4
A = 25
Therefore, when B is 7, A is 25.