Given that 3a=11c and the ratio of b to c 5:7 is work out the ratio a:c (simplest form)

We are given the following:

1. \( 3a = 11c \)
2. The ratio \( \frac{b}{c} = \frac{5}{7} \), but we don't need this to solve for \( \frac{a}{c} \).

### Steps to find \( \frac{a}{c} \):

1. Start with the equation:
   \[
   3a = 11c
   \]

2. Divide both sides by \( c \) to isolate \( a \) in terms of \( c \):
   \[
   \frac{3a}{c} = 11
   \]

3. Now divide both sides by 3:
   \[
   \frac{a}{c} = \frac{11}{3}
   \]

So, the ratio \( a : c \) is \( 11 : 3 \).

Would you like further clarification or more details on this solution?

Here are 5 related questions for practice:
1. If \( 2x = 5y \), what is the ratio of \( x : y \)?
2. If \( 4a = 9b \) and \( \frac{b}{c} = \frac{2}{3} \), find \( a:c \).
3. What is the ratio of \( 7a = 14b \)?
4. Simplify the ratio \( 15x = 20y \).
5. If \( 5a = 8b \) and \( \frac{b}{c} = \frac{3}{5} \), find \( a:c \).

**Tip:** When working with ratios, always simplify the equations first to reduce the ratios to their simplest form!

Given that 3a=11c and the ratio of b to c is 5:7, work out the ratio a:c (simplest form).

Learn how to find the ratio of a:c given the equation 3a = 11c and the ratio of b to c as 5:7. This step-by-step solution covers key algebraic concepts and ratio simplification methods, suitable for students in Grades 8-10.

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