Maths for Diploma Studies

First, we start by creating two equations with the information provided:

We can then substitute the second equation into the first to solve for Tim’s hours:

Solve for Tim:

Knowing Tim’s hours for the week, we can then solve for Mark’s hours by substituting Tim’s hours into either equation. We will use the second equation for this example:

Of course, you could have just subtracted the 20 from 60 to get Mark’s hours but, that wouldn’t have been as much fun! 

As before, we start by writing out two unique equations using the information provided:

First, let’s get a common coefficient:

And now subtract one equation from another:

Rearrange to isolate soda:

OK. Now that we know we sold eight sodas that night, we now need to plug this value into either of the two original equations:

We determined that last Monday, we only sold three beers. It may be time to consider some advertising or perhaps making beer people want to drink!

First, create two equations using the information provided:

Now we get to a common coefficient:

And now subtract one from the other:

Now we rearrange to isolate one day:

We can input this value into our simplest equation:

And rearrange to isolate weekend:

And calculate:

We can look at each sentence as an equation. First, we show how many hL from each tank is needed to produce 2,000 hL of 7% ABV product:

We then need to think in terms of alcohol content. The first tank was at 10% ABV, and the other tank and 6% ABV. In the finished blend, we have 2,000 hL at 7% ABV or 140 hL of alcohol. This makes our two equations:

We start by getting a common coefficient:

And subtracting one equation from the other:

Rearrange to isolate y:

And calculate the value of y:

With this solution, we can then plug the value for y into one of the two original questions. For this example, we will use the first equation:

Rearrange to isolate x:

And then calculate the value of x: