Step-by-step explanation:
Equations:
68.75 = 0.5c + 1.25m
c + m = 100
First, let's get rid of one of the variables. Let's start with the simplest equation first. Let's move a variable, so that only one variable is equal to the rest of the equation.
c + m = 100 to c = -m + 100
(it doesn't matter which variable)
Next, since we have what variable <em>c </em>is equal to, we will now incorporate it into our more complex equation.
68.75 = 0.5(-m + 100) + 1.25 m
Now, to get rid of the parentheses, and just have a regular addition equation with the only variable being <em>m.</em>
68.75 = -0.5m + 50 + 1.25m
Next, we need to make it so that there is only one version of the variables. Just combine the variables together so that the form one cohesive unit.
68.75 = 0.75m + 50
Now, we are going to do the same thing that we did in our first equation (with a mix of the last step we just did), but instead of variables, we are going to do it with the whole numbers instead, and converge them onto one side of the equal sign. Keep in mind that at this step in the process, the variable with it's cohesive unit should be isolated on one side of the equal sign and the other being taken up solely by whole numbers.
118.75 = 0.75m
Now, we just need to make the variable equal to 1 (or just <em>m</em>). So we must either multiply or divide. In this case we will be multiplying both sides by 0.75.
118.75 x 0.75 = 0.75m
So, after this step, you should have an answer of;
89.0625
However, you can't just sell a 0.0625% portion of something to somebody (especially muffins, like come on). Also, the amount of cookies and muffins must be equal to 100 and each variable is in whole numbers (usually).
*Always make sure that when you are done with a problem that you double check it. Usually, with equations like this, you just plug in the variables into the equations, and if they fit both equations, you've done well.
From this point forward, I'm leaving you to your own devices. It's 2:38 a.m. and I need to get up at 7:15. I hope this helps!
= 257
