John bought two types of bulbs A and B at Ksh 60 and Ksh 56 respectly. He bought a total of 50 bulbs of types at a total of Ksh 2872. determine the number of Type A bulbs that he bought.
B = 50 - A
60A + 56(50 - A) = 2872
60A + 2800 - 56A = 2872
4A = 72
A = 18
add up the bulbs and the costs:
A+B = 50
60A+56B = 2872
so now find A.
Well, let's solve this bulb mystery, shall we?
Let's say John bought x bulbs of type A. Since the price of each type A bulb is Ksh 60, the total cost of type A bulbs would be 60x Ksh.
Similarly, John bought 50 - x bulbs of type B, where each type B bulb costs Ksh 56. So, the total cost of type B bulbs would be (50 - x) * 56 Ksh.
The total cost of all the bulbs is given as Ksh 2872, so we can set up an equation:
60x + (50 - x) * 56 = 2872
Now, let me slip into mathematician mode for a moment and solve this equation for you.
Expanding and simplifying the equation gives us:
60x + 2800 - 56x = 2872
Combining like terms:
4x = 72
Dividing both sides by 4:
x = 18
So, John bought 18 bulbs of type A.
Hooray for John's bright decision!
To determine the number of Type A bulbs John bought, we can use a system of equations. Let's denote the number of Type A bulbs as x and the number of Type B bulbs as y.
According to the given information, the cost of Type A bulbs is Ksh 60 and the cost of Type B bulbs is Ksh 56. Thus, we can form the equation:
60x + 56y = 2872 (equation 1)
We also know that John bought a total of 50 bulbs, so the second equation is:
x + y = 50 (equation 2)
To solve this system of equations, we can use substitution or elimination method. Let's solve it using elimination:
Multiply equation 2 by 60 to make the coefficients of x in both equations equal:
60x + 60y = 3000 (equation 3)
Now, subtract equation 3 from equation 1:
60x + 56y - (60x + 60y) = 2872 - 3000
Simplifying:
-4y = -128
Divide both sides by -4:
y = 128 / 4
y = 32
Substituting the value of y back into equation 2:
x + 32 = 50
Subtract 32 from both sides:
x = 50 - 32
x = 18
Therefore, John bought 18 Type A bulbs.