Answer:
The number of bricks is 16 and the number of blocks is 12
Explanation:
Let the number of bricks be x and blocks be y.
Cost of each brick = $0.38
Total cost of x bricks = 0.38*x
Cost of each block = $1.56
Total cost of y blocks = 1.56*y
Total amount spent for the brickyard = $24.80
So,
Total cost of x bricks + Total cost of y blocks = Total amount spent for the brickyard
=> 0.38x + 1.56y = 24.80 ____equation (1)
Total number of items (bricks+blocks) = 28
So,
Number of bricks + Number of blocks = Total number of items
=> x + y= 28 ____equation (2)
We will solve the two equations by the method of elimination.
Let's multiply equation 2 by -0.38
(-0.38)*x + (- 0.38)*y = (-0.38)*(28)
=> -0.38x - 0.38y = -10.64 ____equation (3)
Adding equation 1 to the equation 3, we get
-0.38x - 0.38y + 0.38x + 1.56y = -10.64 + 24.80
Cancelling out -0.38x and +0.38x on the left side, we get
1.56y - 0.38y = 24.80-10.64
=> 1.18y = 14.16
Dividing both sides by 1.18, we get
=
=> y = 12
Plugging in y=12 in the equation 2, we get
x + y= 28
=> x + 12 =28
Subtracting 12 from both sides, we get
x+ 12 -12 = 28- 12
Cancelling out the +12 and -12 from the left side, we have
x = 16
So, the number of bricks is 16 and the number of blocks is 12.