Let's use grouping techniques to find the weight of a circle C and a triangle T. First, let's combine like terms to rewrite the equation. We can combine the C terms. 2 C + C gives us 3 C. We also have 2 + 2, which equals 4. We can simplify this equation to 3 C + 4 = T.
Now, let's simplify the second equation.
The scale shows two boxes, each with a weight of t + 10, balanced by a single weight of 40. Since two boxes of weight t + 10 balance 40, one of them must balance 20. So, we can write t + 10 = 20.
We now have two simplified equations.
The first is 3 c + 4 = t and the second is t + 10 = 20. Our second equation only contains t. So we can find the weight of the triangle first.
To solve t + 10= 20, let's subtract 10 from both sides. Then we get t = 10.
Now we can use the value of t to find c.
Substituting 10 for t in our first equation, we get 3 c + 4 = 10. We can subtract four from both sides. Now we have 3 c = 6. By dividing both sides by 3, we get C= 2.
The weight of a circle is 2 and the weight of a triangle is 10. We solved a system of equations by first simplifying and then using substitution.