A box of Brand A laundry detergent washes 20 loads of laundry and costs $6. A box of Brand B laundry detergent washes 15 loads of laundry and costs $5.
In the ratio tables that follow, fill in equivalent rates of loads washed per dollar. Include some examples where the number of loads washed is less than 15 and the cost is less than $5. Explain your reasoning.
For Brand A, the top is 20 loads and the bottom is $6.
For Brand B, the top is 25 loads and the bottom is $5.
Let's say for Brand A, I have 20 loads and it costs $6, the next load will be 3.33 that costs $1. How would I keep going to find the next load and the costs of that load? For Brand B, I have 15 loads that costs $5 and the next load is 3 that costs $1, how would I find the next loads and costs?
For Brand A: loads washed is 20 divided by 6 to get to the next load which is 3.33 and the costs is $6 divided by 6 which is 1. So the next load is 3.33 that costs $1. For Brand A: loads washed is 20 divided by 20 to get to the next load which is 1 and the costs is $6 divided by 20 which is $0.30. So the next load is 1 that costs $0.30
For Brand B: loads washed is 15 divided by 5 to get to the next load which is 3 and the costs is $5 divided by 5 which is $1. So the next load is 3 that costs $1. For Brand A: loads washed is 15 divided by 15 to get to the next load which is 1 and the costs is $5 divided by 15 which is $0.33. So the next load is 1 that costs $0.33
How would I keep going where the number of loads washed is less than 15 and the cost is less than $5
To continue the ratio tables where the number of loads washed is less than 15 and the cost is less than $5, we can use the same approach of dividing the current number of loads washed by the current cost.
For Brand A:
To find the next load and cost where the number of loads is less than 15 and the cost is less than $5, we can use the following steps:
1. Divide the current number of loads washed (e.g., 15) by the current cost (e.g., $5) to get the rate of loads washed per dollar (e.g., 15/5 = 3).
2. The next load will be 3, as we obtained in step 1, and the cost will be $1 (since we are finding the loads per dollar ratio).
3. Repeat step 1 and step 2 until the desired condition (loads washed less than 15 and cost less than $5) is met.
For example, continuing from the given numbers:
- 15 loads washed and $5 cost: loads washed per dollar = 15/5 = 3
- The next load will be 3 and the cost will be $1: loads washed per dollar = 3/1 = 3
- The next load will be 1 and the cost will be $0.33: loads washed per dollar = 1/0.33 ≈ 3.03
By following this process, you can continue filling in the ratio table for Brand A with loads washed per dollar, ensuring the loads washed are less than 15 and the cost is less than $5.
Similarly, you can apply the same steps for Brand B, starting with the given numbers (15 loads washed and $5 cost), and continue until the desired condition is met.