Suppose that a crayon weighs the same as a marker. You have a box of crayons, 4 extra crayons, and 20 markers. Let b be the number of crayons in the box. A scale balances with all the crayons on one side and all the markers on the other. You remove markers from the scale so that you can color a picture. Find how many crayons you must remove to keep the scale balanced. Then complete the equation.
b+4−___=18
How many crayons must you remove to keep the scale balanced?
12
To solve this problem, we need to understand that the weight of a crayon is equal to the weight of a marker.
Let's break down the information we have:
- We have a box with "b" number of crayons.
- We have 4 extra crayons.
- We have 20 markers.
- The scale balances when both sides have the same weight.
We want to find out how many crayons we must remove from the scale to keep it balanced.
First, let's determine the weight of the crayons and markers. Since both weigh the same, we can assign a variable to represent their weight.
Let's say the weight of a crayon or a marker is "x."
The total weight on the left side of the scale, with all the crayons, is the weight of the box with crayons (b) plus the weight of the extra crayons (4):
Total weight on the left side = b * x + 4 * x = (b + 4) * x
The total weight on the right side of the scale, with all the markers, is the weight of the markers (20):
Total weight on the right side = 20 * x
Since the scale balances, the total weight on both sides is the same:
(b + 4) * x = 20 * x
Now, let's solve for "b" to find the number of crayons we must remove to keep the scale balanced:
b + 4 = 20
To isolate "b", we subtract 4 from both sides:
b = 20 - 4
b = 16
Therefore, we must remove 16 crayons from the scale to keep it balanced.
To complete the equation b + 4 - ___ = 18, we substitute the value we found:
16 + 4 - ___ = 18
Now, we can solve for the missing value by isolating the variable:
20 - ___ = 18
-___ = 18 - 20
-___ = -2
Therefore, we must remove 2 crayons to keep the scale balanced.
The completed equation is:
16 + 4 - 2 = 18