Look at the pictures of the scales below. Can you write equations to represent what you see on each scale? Can you figure out the weight of the green block? Can you figure out the weight of the blue block? In this section, we will learn how to work with equations that represent what we see on scales.
In order to solve the problem above, we can write equations to represent what we see on each scale. We know that if we add the weights of each of the blocks on one scale together, the total weight must be the same as the number on the scale.
If we look at the scale on the left, we see that there are two green blocks that weigh 8 pounds total. An equation would be:
There is another way to think about the equation.
This means, I could also write the equation as:
In the following examples, we will practice writing equations in different ways and matching equations with scales.
1. Fill in the number to finish the equation:
On the left side of the equation we see three 3 blocks. This means, we need a 3 on the right side of the equation next to the red block. The equation should look like this:
2. Circle the equation that matches the scale:
On the scale we see two red blocks and one yellow block. They add up to 20 pounds. The correct equation should have 2 red blocks and one yellow block. The correct equation is c.
3. Eric wrote these equations from pictures of scales. Use Eric’s equations. Find the weight of each block.
From the first equation we can see that 2 blue blocks weigh 6 pounds. This means that each blue block is 3 pounds.
From the second equation we can see that one yellow block and one blue block together weigh eight pounds. Since we know that the blue block is 3 pounds, we have this equation: yellow block +3=8
Because 5+3=8, we know that the yellow block must be 5 pounds. Here is our final answer:
Earlier Problem Revisited
We can use problem solving steps to help:
In math, an unknown is a letter that stands for a number that we do not yet know the value of. In this concept, the blocks that we did not know the weights of were unknowns. An equation is a math sentence that tells us two quantities that are equal. In this concept, we wrote equations with unknowns to represent what we saw on the scales.
Write equations for each scale. Figure out the weight of each block.
Fill in the numbers to make an equation.
Circle the equation that matches the scale.
Eric wrote these equations from pictures of scales. Use Eric’s equations. Find the weight of each block.
For each of the following, write equations. Figure out the weights of the blocks.
Fill in the numbers for problems 6-9.
Circle the equation that matches the scale for problems 10 and 11.
Eric wrote these equations in problems 12 and 13 from pictures of scales. Use Eric’s equations. Find the weight of each block.
For problems 14-16, write the block equation for each scale. Figure out the weights of the blocks.