a brick is placed on a balance scale.it balances exactly with a 3/4 pound weight and 3/4 of a brick .what is the weight of the brick? show and explain work
x = 3/4 x + 3/4
1/4 x = 3/4
x = 3
brick= (3/4)+(3/4)
brick=(6/4)=1.5
To find the weight of the brick, we can use a bit of algebraic reasoning. Let's assume the weight of the brick is "x" pounds.
Based on the given information, we know that the brick's weight balances exactly with a 3/4 pound weight and 3/4 of the brick. So, the weight of the 3/4 brick can be represented as 3/4 * x (since we assumed the weight of the brick is "x" pounds).
Now, let's set up the equation for the balance scale:
3/4 * x = 3/4
To find the value of "x" (the weight of the brick), we need to isolate it on one side of the equation.
To do so, we can divide both sides of the equation by 3/4, which is the same as multiplying by its reciprocal (4/3):
(3/4 * x) * (4/3) = (3/4) * (4/3)
On simplifying, we get:
(x * 4) / (4 * 3) = 3/4
Now, cancel out the common factor of 4:
x / 3 = 3/4
Next, multiply both sides of the equation by 3 to further isolate "x":
(x / 3) * 3 = (3/4) * 3
You will end up with:
x = 9/4
So, the weight of the brick is 9/4 pounds.