SUPER confused on this one Math Question, help please !

For the trucking cost you only have a reduction in cost that equals to 50% of the 95% so you can calculate the savings simply by multiplying 95% by 50%

If you only had a cost reduction for the refining cost you would be able to calculate this the same way but since you also have an increase in price you will have to add that to the remaining cost, before you can calculate the savings.

1.  Calculate the reduction in cost by 50% (1*0.5)

2. Add the price increase, which gives you the new cost (0.5*1.25 = 0.625)

3. Calculate the difference between old and new cost (1-0.625 = 0.375)

Hope this helps :)

Hey ?

Totally valid confusion—and you're actually very close to getting it. Here’s the clear rule you can use to understand when to subtract from 1 vs when to take a direct product:

✅ Rule of thumb:

? If the question is asking for cost savings as a percentage of the original, then:

• You always want to end up comparing the new cost to the original cost
• So if the cost goes from X → Y, then cost savings = (X - Y) / X = 1 - (Y / X)

Let’s now look at your examples:

? Trucking:

Trucking is 10% of Total Cost, and within that:

• 5% is Fixed → unaffected
• 95% is Variable → reduced by 50%

So within Trucking, your new cost is: 0.05 + 0.95 * 0.5 = 0.05 + 0.475 = 0.525

That means total Trucking cost is now 52.5% of what it was before, or a 47.5% reduction → and that’s what they wrote.

? They wrote 95% x 50% = 47.5% savings, which skips a step but is mathematically the same because only 95% of cost is affected.

? Refining:

You start with cost = X

Step 1: You’re refining half the sugar beets → cost becomes 0.5X

Step 2: But now the per-unit cost increases by 25% → cost becomes: 0.5X * 1.25 = 0.625X

So now the cost is 62.5% of original → savings = 1 - 0.625 = 0.375 = 37.5%

? Here, the changes are sequential multipliers that act on the total cost, so you must calculate the end result, then subtract to get the savings.

? So when to subtract from 1?

Whenever you're calculating "savings", or "reduction" as a percentage of the original—you’ll always want to do:

Savings % = 1 - (new cost / original cost)

The trucking shortcut only works cleanly if you’re applying a single % cut to a part of the cost.

Let me know if you'd like to go through more examples or build an easy cheat sheet for these types of questions ?

Best,
Alessa ?

When do we do “1 – …” vs. just take the percentage?

In both situations, the underlying concept is:

Savings % = 1 - (Fraction Remaining)

• If you have the fraction (or percent) that remains (like 0.625 → 62.5%), you do 1 - 0.625 = 0.375 (37.5% savings).
• If, on the other hand, you already computed how much is saved (like 0.95 * 0.50 = 0.475 → 47.5% saved), then you’re already at the final “savings fraction” and don’t need to do “1 – …”.

So it’s not that “one scenario must do it, and the other must not.” It’s just a different presentation style:

• Trucking: The write-up jumped straight to the fraction saved: 95% * 50% = 47.5%.
• Refining: The write-up jumped straight to the fraction remaining (0.625) and then subtracted from 1 to get 37.5%.

Either approach works; they’re just different ways of doing the fraction arithmetic. Whenever you see “we have a new fraction of the original left,” you do 1 - (that fraction) to see how much was removed/saved. Whenever you see “we are cutting X% out of a portion,” that already is the portion saved.

Trucking cost savings: 

Initial Cost: 95% + 5% = 100%

Final Cost: 95% * 50% + 5% = 52.5%

Savings = Initial Cost - Final Cost = 100% - 52.5% = 47.5%

Refining cost savings: 

Initial Cost: 100%

Final Cost: 100% * (1 + 25%) * 50% = 62.5%

Savings = Initial Cost - Final Cost = 100% - 62.5% = 37.5%

So what's different vs. your casebook? In the truck savings it calculated the savings directly. In the refining savings it calculated the new cost (not the savings), so you need to do an additional calculation to get the savings.