Write a basic percent problem, the solution to which can be found by solving the equation $$ 81=0.64 \cdot n $$. 64 is $$ 81 \% $$ of what number? What number is $$ 64 \% $$ of 81 ? 81 is $$ 64 \% $$ of what number? What percent of 81 is 64 ?

Question

UpStudy AI · Accepted Answer

Let's break down the problem step by step.

### Given Equation
The equation provided is:
$$
81 = 0.64 \cdot n
$$

### Step 1: Solve for $$ n $$
To find $$ n $$, we can rearrange the equation:
$$
n = \frac{81}{0.64}
$$

Now, let's calculate $$ n $$.

### Step 2: Calculate $$ n $$
Using the equation:
$$
n = \frac{81}{0.64}
$$

I'll perform the calculation now.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{81}{0.64}$$
- step1: Convert the expressions:
  $$\frac{81}{\frac{16}{25}}$$
- step2: Multiply by the reciprocal:
  $$81\times \frac{25}{16}$$
- step3: Multiply:
  $$\frac{81\times 25}{16}$$
- step4: Multiply:
  $$\frac{2025}{16}$$
The calculation gives us:
$$
n = 126.5625
$$

### Interpretation of the Results
Now, let's interpret the results based on the questions posed:

1. **64 is $$ 81\% $$ of what number?**
   - From our equation, we found that $$ n = 126.5625 $$. Therefore, 64 is $$ 81\% $$ of $$ 126.5625 $$.

2. **What number is $$ 64\% $$ of 81?**
   - To find this, we calculate:
   $$
   0.64 \cdot 81
   $$
   Let's calculate that now.
Calculate the value by following steps:
- step0: Calculate:
  $$0.64\times 81$$
- step1: Multiply the numbers:
  $$51.84$$
The calculation gives us:
$$
0.64 \cdot 81 = 51.84
$$
Thus, $$ 64\% $$ of $$ 81 $$ is $$ 51.84 $$.

3. **81 is $$ 64\% $$ of what number?**
   - We can set up the equation:
   $$
   81 = 0.64 \cdot m
   $$
   Rearranging gives:
   $$
   m = \frac{81}{0.64}
   $$
   We already calculated this earlier, and we found $$ m = 126.5625 $$.

4. **What percent of 81 is 64?**
   - To find this, we can use the formula:
   $$
   \text{Percent} = \left( \frac{64}{81} \right) \cdot 100
   $$
   Let's calculate that now.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{64}{81}\times 100$$
- step1: Multiply:
  $$\frac{64\times 100}{81}$$
- step2: Multiply:
  $$\frac{6400}{81}$$
The calculation gives us:
$$
\text{Percent} \approx 79.012346
$$
Thus, $$ 64 $$ is approximately $$ 79.01\% $$ of $$ 81 $$.

### Summary of Results
1. **64 is $$ 81\% $$ of what number?** $$ 126.5625 $$
2. **What number is $$ 64\% $$ of 81?** $$ 51.84 $$
3. **81 is $$ 64\% $$ of what number?** $$ 126.5625 $$
4. **What percent of 81 is 64?** Approximately $$ 79.01\% $$
64 is 81% of 126.5625. 64 is 79.01% of 81.

Write a basic percent problem, the solution to which can be found by solving the equation \( 81=0.64 \cdot n \). 64 is \( 81 \% \) of what number? What number is \( 64 \% \) of 81 ? 81 is \( 64 \% \) of what number? What percent of 81 is 64 ?

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