The recipe calls for a ratio of 2 parts borax, 2 parts washing soda, and 1 part soap flakes. This means for every 1 part of soap flakes, there are 2 parts of borax and 2 parts of washing soda combined.
If Lenny uses 7 cups of soap flakes, we need to calculate the amount of borax and washing soda he needs.
Since there are 2 parts of each for every 1 part of soap flakes, he will need:
- Borax: 2 parts
- Washing soda: 2 parts
So combined, he needs a total of \(2 + 2 = 4\) parts for every 1 part of soap flakes.
Now we can set up a ratio:
\(\text{Total Parts} = 2 \text{ (Borax)} + 2 \text{ (Washing Soda)} + 1 \text{ (Soap Flakes)} = 5 \text{ parts}\)
Since he is using 7 cups of soap flakes (1 part), we can find out how much borax and washing soda he needs:
To find out how many cups 4 parts would be, we can use the following formula:
\[ \text{Cups of Borax and Washing Soda} = \text{Cups of Soap Flakes} \times 4 \]
Substituting in the value:
\[ \text{Cups of Borax and Washing Soda} = 7 \times 4 = 28 \text{ cups} \]
So, the total amount of borax and washing soda combined that Lenny needs is 28 cups.