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
Well, it seems like you've got the gist of it! Let me help you find a few more examples for both brands.
For Brand A: We already know that 20 loads cost $6, and the next load is 3.33 that costs $1. If we continue the pattern, the load after that would be 1 that costs $0.30, and then we can have 0.9 loads that cost $0.20. So you can see that as the loads decrease, the cost decreases as well.
For Brand B: It starts with 15 loads costing $5, and the next load is 3 that costs $1. If we keep going, the load after that would be 1 that costs $0.33, and then we can have 0.8 loads that cost $0.20. Again, as the loads decrease, the cost decreases too.
So you can see that both brands follow a similar pattern with decreasing loads and costs. And hey, with these lower loads, you might just be able to squeeze in doing laundry while juggling a few extra tasks. Multitasking at its finest!
To find the next loads and costs for Brand A laundry detergent, you need to continue dividing the total loads washed (20) by the total cost ($6).
So, for example, to find the loads and cost for the next load after 20 loads, you would divide 20 by 6. This gives you 3.33, which means you can wash approximately 3.33 loads for every $1.
To find the cost for this next load, you would divide $6 by 6, which equals $1. So, the next load would be 3.33 loads that cost $1.
Similarly, to find the loads and cost for the load after that, you would divide 3.33 by 6 and $1 by 6.
Continuing this pattern, you can find the loads and costs for any number of loads less than 20.
For Brand B laundry detergent, you follow the same process. Divide the total loads washed (15) by the total cost ($5) to find the rate of loads washed per dollar.
To find the next loads and costs, divide 15 by 5. This gives you 3, meaning you can wash approximately 3 loads for every $1.
To find the cost for this next load, divide $5 by 5, which equals $1. So, the next load would be 3 loads that cost $1.
To find the loads and costs for subsequent loads, you continue dividing 3 by 5 and $1 by 5.
Following this logic, you can determine the loads and costs for any number of loads less than 15.