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
To find the equivalent rates of loads washed per dollar for each brand, we need to divide the number of loads by the cost of the detergent. Let's start with Brand A:
Brand A:
Top number: 20 loads
Bottom number: $6
To find the loads washed per dollar, we divide the top number (loads) by the bottom number (cost):
Equivalent rate = 20 loads / $6
Now, let's simplify the fraction:
Equivalent rate = (20/2) loads / ($6/2)
Equivalent rate = 10 loads / $3
The equivalent rate for Brand A is 10 loads per dollar.
Now let's move on to Brand B:
Top number: 15 loads
Bottom number: $5
Equivalent rate = 15 loads / $5
Equivalent rate = (15/5) loads / ($5/5)
Equivalent rate = 3 loads / $1
The equivalent rate for Brand B is 3 loads per dollar.
To provide examples where the number of loads is less than 15 and the cost is less than $5, we can create equivalent ratios:
For Brand A:
Let's say we have 10 loads.
Equivalent cost = 10 loads / 10 loads per dollar
Equivalent cost = 1 dollar
So for 10 loads, the cost would be $1 for Brand A.
For Brand B:
Let's say we have 6 loads.
Equivalent cost = 6 loads / 3 loads per dollar
Equivalent cost = 2 dollars
So for 6 loads, the cost would be $2 for Brand B.
These examples provide instances where the number of loads and the cost are both less than the given values, showcasing the flexibility of the ratios.