Let's see how to represent an unknown weight using algebra. The letter C stands for the weight of one circle.
Since each circle weighs C, we could add them up. C plus C plus C plus C. But a more direct way to express this is with multiplication. The total weight is the weight of one circle C multiplied by the number of circles which is four.
In algebra, we have a standard notation.
We write the number or coefficient before the variable. We also omit the multiplication symbol. So C * 4 is typically written as 4 C. Now let's solve for a specific value. On this scale, we have four circles with a combined weight of 4 C plus a standard weight of three. The total weight on the scale is 11.
To find the weight of just the circles, we can subtract 3 from the total weight.
11 - 3 = 8. So now we know the four circles by themselves weigh 8.
This gives us a simpler equation. 4 C = 8. To find the weight of one circle, we can ask what number multiplied 4 gives us 8. We find this by dividing 8 by 4, which gives us two. So the weight of a single circle C is two. Let's look at another scenario. On the scale, we have one circle C and one triangle T. The total weight on the scale is 12. Since both objects are on the scale together, their total weight is the sum of their individual weights. The correct equation is C + T= 12.
Now let's solve for an unknown. The problem states that a circle weighs 2.
We can substitute this value into our equation. c + t = 12. This gives us the equation 2 + t = 12. To find t, subtract 2 from both sides of the equation. 12 - 2 is 10. So, one triangle weighs 10.
We've seen how scale problems can be represented and solved using equations.
By building these equations, you can systematically find the values of any unknowns.
