Finding the Part Problems

Question

Use the basic percent formula to complete the problems below. Show all work.

1. Find 12% of 34.

2. Alivia bought a new softball glove for 65% off the original price of $34. How much did she pay for the glove? Round to the nearest cent, if necessary.

3. Find 72.5% of 327. Round to the nearest tenth, if necessary.

4. A secretary's hourly wage was $15.00 before a 9% raise. What is the new hourly wage?

5. Only 0.7% of the students in a class of 164 have green eyes. How many students have green eyes? Round to the nearest whole number, if necessary.

6. 150% of 64 is what number? Round to the nearest tenth, if necessary.

7. A welder's hourly wage was $32.00 before a 6% raise. What is the new hourly wage?

Answer 1

Another way to look at "%", or "percent", is to break down the word to "per cent" with the understanding that whenever you see "per" it implies "divided by" ("/", symbolically); and whenever you see "cent", it has something to do with the number "100", from Latin based languages. For example: If I earn $4 per hour, I earn $4/1hr or $4/60min, where 1hour=60minutes. For another example, if I travel 60 miles in 2 hours, my speed is 60miles/2hours or 30miles/hour or 30 miles "per" hour. So think of "percent" as "per 100" or "divided by 100".

Another principle is that the word "of" in a numerical problem, can be translated as "multiplied by".

Finally, whenever you see the word "percent" it is always a "percent OF" something, either specifically stated or implied.

So, 12% of 34 is 12 percent of 34 or (12/100)X(34)

65% off $34 is tricky because "off" is not "of". "off" means "subtracted from". Since the % has to be "of" something, your have to ask, "What is 65% a percent "of"?, if not specifically so stated. In this case, the 65% is implied to be "of" the $34. So we are subtracting 65% of $34 from $34. Performing this arithmetically:

$34-(65% of $34)

$34-(65 percent of $34)

$34-(65/100)($34)

$34-$(65)(34)/100

$34-$22.10=$11.90

Keep in mind that, in decimal form, "percent" as "dividing by 100, functionally means moving the decimal point to the left 2 places. So, in place of 64%, or 64/100, we could have written "0.64".

$34-(65% of $34)

$34-(0.65)($34)

$34-$22.10=$11.90

We also could have used the distributive property:

$34-(0.65)($34)

$34(1-0.65)

$34(0.35)=$11.90

With familiarity, one can go from 65% directly to 0.65 automatically when writing out a "percent" problem arithmetically.

In 4. and 7., ask what the percentage is "of", then multiply that by the number of the percent divided by 100 (either fractionally or decimally) to find how much the raise was in actual value to add to the original wage.

Answer 2

You'll want to utilize the folowing formula:

% = (part / whole) x 100

The main challenge with these problems is identifying the part and/or the whole components and plugging these into the right spots. For example, if we take #2:

2. Alivia bought a new softball glove for 65% off the original price of $34. How much did she pay for the glove? Round to the nearest cent, if necessary.

Using our equation, we have: 65 = (part / 34) x 100

In other words, they are asking what "part" of the original price (or "whole": $34) would represent 65% off --> this would mean that she would pay 35% of the original price:

Solving for the "part" she would pay (p) of the original price:

35 = (part / 34) x 100 (divide both sides by 100)

35 / 100 = p / 34 (multiply both sides by 34)

p = 11.9

Therefore, she paid $11.90 for the glove.

Hope this helps!

Best,

Todd