If a is 5% of b, b is 24% of c. If a=480. Find the value of b & c.

We are given:

- \( a = 5\% \) of \( b \), which means \( a = 0.05b \)
- \( b = 24\% \) of \( c \), which means \( b = 0.24c \)
- \( a = 480 \)

Let's solve this step-by-step.

### Step 1: Find the value of \( b \)
From the first equation \( a = 0.05b \), substitute \( a = 480 \):

\[
480 = 0.05b
\]

Solve for \( b \):

\[
b = \frac{480}{0.05} = 9600
\]

### Step 2: Find the value of \( c \)
From the second equation \( b = 0.24c \), substitute \( b = 9600 \):

\[
9600 = 0.24c
\]

Solve for \( c \):

\[
c = \frac{9600}{0.24} = 40000
\]

### Final Values:
- \( b = 9600 \)
- \( c = 40000 \)

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. What is the percentage relationship between \( a \) and \( c \)?
2. If \( b \) were increased by 10%, what would the new value of \( c \) be?
3. What would happen to \( c \) if \( a \) doubled while the percentages remained the same?
4. How would the value of \( b \) change if \( a \) were 6% of \( b \)?
5. Can you express \( c \) as a function of \( a \) without intermediate steps?

**Tip:** Always double-check the units or percentages involved in word problems to avoid mistakes.

Learn how to find the values of b and c given the problem 'If a is 5% of b, and b is 24% of c, with a = 480.' This problem involves understanding percentages and basic algebra. A step-by-step solution is provided, suitable for students in Grades 6-8.

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