To determine which two packages have the same ratio of cartridges to cost, we will follow these steps.
### Step 1: Define the Packages
First, let's list out the data for each package:
- Package A: 3 cartridges for \[tex]$60
- Package B: 6 cartridges for \$[/tex]60
- Package C: 1 cartridge for \[tex]$20
- Package D: 3 cartridges for \$[/tex]20
### Step 2: Calculate the Ratio of Cartridges to Cost
Next, we calculate the ratio of cartridges to cost for each package. The formula for the ratio is:
[tex]\[ \text{Ratio} = \frac{\text{Number of Cartridges}}{\text{Total Cost}} \][/tex]
Let's perform the calculations:
- Package A:
[tex]\[ \text{Ratio}_A = \frac{3}{60} = 0.05 \][/tex]
- Package B:
[tex]\[ \text{Ratio}_B = \frac{6}{60} = 0.1 \][/tex]
- Package C:
[tex]\[ \text{Ratio}_C = \frac{1}{20} = 0.05 \][/tex]
- Package D:
[tex]\[ \text{Ratio}_D = \frac{3}{20} = 0.15 \][/tex]
### Step 3: Compare the Ratios
Now, we compare the ratios to identify which pairs of packages have the same ratio:
- Package A and B:
[tex]\[ 0.05 \neq 0.1 \][/tex]
- Package A and C:
[tex]\[ 0.05 = 0.05 \][/tex]
- Package A and D:
[tex]\[ 0.05 \neq 0.15 \][/tex]
- Package B and C:
[tex]\[ 0.1 \neq 0.05 \][/tex]
- Package B and D:
[tex]\[ 0.1 \neq 0.15 \][/tex]
- Package C and D:
[tex]\[ 0.05 \neq 0.15 \][/tex]
### Conclusion
The pairs that have the same ratio of cartridges to cost are:
[tex]\[ \boxed{\text{Packages A and C}} \][/tex]
