Sure, I can explain the step-by-step solution to this problem!
1. First, let's understand the given information:
- Eliza makes 8 tablespoons of sauce for every 12 pork chops.
2. We need to find out how many pork chops Eliza will make if she prepares 12 tablespoons of sauce. To do this, we need to understand the ratio of sauce to pork chops:
- The ratio of sauce to pork chops given is 8 tablespoons of sauce for every 12 pork chops. We can represent this ratio as 8:12.
3. Next, we simplify the ratio 8:12 to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
- [tex]\( \frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \)[/tex]
This means for every 2 tablespoons of sauce, Eliza makes 3 pork chops.
4. Now, we'll create a proportion to solve for the number of pork chops when Eliza uses 12 tablespoons of sauce. Let's denote the number of pork chops as [tex]\( x \)[/tex]:
- The proportion based on the simplified ratio (2 tablespoons of sauce to 3 pork chops) is:
[tex]\[
\frac{2}{3} = \frac{12}{x}
\][/tex]
5. To solve for [tex]\( x \)[/tex], we can cross-multiply and then divide:
[tex]\[
2x = 3 \times 12
\][/tex]
[tex]\[
2x = 36
\][/tex]
[tex]\[
x = \frac{36}{2}
\][/tex]
[tex]\[
x = 18
\][/tex]
So, if Eliza prepares 12 tablespoons of sauce, she will make 18 pork chops.
