You were busy working on a problem using 4 big squares, 8 rectangles, and 8 small squares. Your partner accidentally knocked some algebra tiles off the your desk. You now have 1 big square, 3 rectangles, and 5 small squares on your desk.

Write and algebraic equation that shows what tiles you began with, what you partner knocked off the desk, and how many tiles you have left.

errrr, I don't get it?

help ?

begin --> 4b+8r+8s

knocked xb+yr+zs
end ----> (4-x)b+(8-y)r +(8-z)s =1b+3r+5s

so
(4-x)=1 so x = 3
(8-y)=3 so y = 5
(8-z)=5 so z = 3

Sure! Let's break down the problem step by step to help you understand.

Step 1: Determine what tiles you began with.
According to the problem statement, you initially had 4 big squares, 8 rectangles, and 8 small squares.

Step 2: Determine what your partner knocked off the desk.
Your partner accidentally knocked off 3 big squares, 5 rectangles, and 3 small squares.

Step 3: Determine how many tiles you have left.
Currently, you have 1 big square, 3 rectangles, and 5 small squares on your desk.

Now, let's write an algebraic equation to represent the situation:

Let B represent the number of big squares.
Let R represent the number of rectangles.
Let S represent the number of small squares.

Initially, you had:
4B + 8R + 8S

Your partner knocked off:
-3B - 5R - 3S

Now, you have:
1B + 3R + 5S

The equation representing the tiles you began with, what your partner knocked off, and how many tiles you have left can be written as:

(4B + 8R + 8S) - (3B + 5R + 3S) = 1B + 3R + 5S

Simplifying the equation, we have:
4B + 8R + 8S - 3B - 5R - 3S = 1B + 3R + 5S

Combining like terms on both sides:
B + 3R + 5S = 1B + 3R + 5S

The equation simplifies further to:
B = B

Therefore, the equation B = B represents the tiles you began with, what your partner knocked off, and how many tiles you have left. This equation shows that the number of big squares you have at the end is the same as the number you began with.