Translate to a proportion: What percent of 32 is 20? Let p= the percent.
The Correct Answer and Explanation is:
To solve the problem “What percent of 32 is 20?”, we need to set up a proportion where ppp represents the percent.
We know that:
- “p percent of 32” is the same as p100×32\frac{p}{100} \times 32100p×32.
- We are given that this equals 20.
So, we set up the equation: p100×32=20\frac{p}{100} \times 32 = 20100p×32=20
Now, we solve for ppp:
- Multiply both sides by 100 to eliminate the denominator:
p×32=20×100p \times 32 = 20 \times 100p×32=20×100 p×32=2000p \times 32 = 2000p×32=2000
- Now, divide both sides by 32:
p=200032p = \frac{2000}{32}p=322000 p=62.5p = 62.5p=62.5
So, 62.5% of 32 is 20.
Explanation:
The problem is asking for what percent 20 is of 32. This is essentially saying, “If I take 32 and find a certain percentage of it, that percentage results in 20.” By expressing it as a proportion, we can solve for ppp, the percentage.
In this case, the proportion p100×32=20\frac{p}{100} \times 32 = 20100p×32=20 reflects that the fraction of 32 that equals 20 corresponds to ppp percent. This solution shows that p=62.5p = 62.5p=62.5, so 62.5% of 32 equals 20.
