The problem in the image asks to evaluate the expression $5a - 7b$ given a set of conditions for the variables $a$, $b$, $c$, $d$, $e$, and $f$. The conditions are:

• $a = c^2$
• $b = d - 9$
• $c = 2e$
• $d = 4f$
• $e = 3$
• $f = 5$

Let's go through the steps to find the value of $5a - 7b$:

1. Determine the value of $e$ and $f$:

   • $e = 3$
   • $f = 5$

2. Calculate $c$:

   • $c = 2e = 2 \times 3 = 6$

3. Calculate $d$:

   • $d = 4f = 4 \times 5 = 20$

4. Calculate $a$:

   • $a = c^2 = 6^2 = 36$

5. Calculate $b$:

   • $b = d - 9 = 20 - 9 = 11$

6. Substitute $a$ and $b$ into the expression $5a - 7b$:

   • $5a = 5 \times 36 = 180$
   • $7b = 7 \times 11 = 77$
   • $5a - 7b = 180 - 77 = 103$

So, the value of $5a - 7b$ is 103.

Would you like further details or have any questions? Here are some related questions to consider:

1. How would the result change if $f$ were doubled?
2. What is the impact on the expression $5a - 7b$ if $e$ were reduced by half?
3. How would the expression change if the condition for $d$ was $d = 3f$ instead of $d = 4f$?
4. What happens to $5a - 7b$ if the value of $c$ were tripled?
5. How does changing $b = d + 9$ affect the final outcome of the expression?

Tip: When substituting values into an expression, always follow the order of operations carefully to avoid mistakes.