Hello mathematicians!
Today I was caught off guard with a 4th grade question and I think I solved it. Now after taking a look at this and thinking, I was really shocked at how stupid I was, is or still am. Since I am in a college mathematics, doing functions and stuff but this had me the most stressed out as I could ever be. Because it was my little cousin's homework! I mean 14th grader can't even do 4th grades mathematics? Am I stupid?
Question:
The sum of $9$ shapes is $30$. There are $6$ circles and $3$ squares. What are the values of the shapes? (nothing else is given)
$6$ Circles + $3$ Squares = $30$
My calculation:
Now I thought, oh hey it's a easy question and I did this.
$$6a + 3b = 30$$
$$6a = 30-3b$$
$$a = 5-0.5b$$
$$6 \times (5-0.5b) + 3b = 30$$
However, I get zero trying to solve for $a$ and $b$.
So my theory is that there is no right answer, you can simply say the value for each circle is $3$, then $3 \times 6 = 18$ and $30 - 18 = 12$, so the value for each square is $4$. And you can find it with any numbers.
So is my theory right? or am I stupid because this is a very laughable equation for a college student? But for me, well I think I am stupid.
Appreciate your time in reading and solving my question.
-Thanks
Your solution doesn't work because you isolated $a$ in the equation then substituted it back into the same equation. The result is a tautology (not zero, that wouldn't satisfy $6a+3b=30$.)
There isn't a second equation given to do an algebraic solution. So forget you know algebra; just start guessing and checking. A multiple of $6$ plus a multiple of $3$ equals $30$. I stumbled on $a=4$ and $b=2$ after a bit. Since $6$ is a multiple of $3$, you can find more solutions by decreasing $a$ by $1$ and increasing $b$ by $2$.