Mike…check the wording on this Q (#37; section4). I lose track of what it’s asking for. Can you break it down? Tks!

The value of r is 20/21 times the value of t, where t>0. The value of t is what percent greater than the value of r?

Sure thing. To start, we gotta carefully translate the first sentence. Remember, “is” in a sentence means “=”.


So far so good?

Now let’s deal with the question sentence. It’s asking what percent greater one number is than another number–that’s a percent change question. Another way of asking it would be: what’s the percent change between r and t?

Which we would figure out by plugging the values into the percent change formula:

Since we know t is the bigger number, we rewrite thusly:

\dfrac{t-r}{r}\times 100\%

Now we can use the first translation we did to plug in. It’s gonna get a little messy for a minute.

\dfrac{\left(t-\frac{20}{21}t\right)}{\left(\frac{20}{21}t\right)}\times 100\%\\\\\\=\dfrac{\left(\frac{1}{21}t\right)}{\left(\frac{20}{21}t\right)}\times 100\%\\\\\\=\dfrac{\left(\frac{t}{21}\right)}{\left(\frac{20t}{21}\right)}\times 100\%

Now remember when you divide fractions you multiply reciprocals, so we can rewrite:

\dfrac{\left(\frac{t}{21}\right)}{\left(\frac{20t}{21}\right)}\times 100\%\\\\\\=\dfrac{t}{21}\times \dfrac{21}{20t}\times 100\%\\\\=\dfrac{1}{20}\times 100\%\\\\=0.05\times 100\%\\\\=5\%

That means t is 5% greater than r.

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