A baker must spend no more than $400 to order eggs for cookies and cupcakes. Supplies for each batch of cookies costs $2, and supplies for each batch of cupcakes costs $10. This relationship is shown in the graph. The baker needs to make at least 20 more batches of cookies than cupcakes. Which choice is a reasonable solution?
60 batches of cookies and 40 batches of cupcakes
20 batches of cookies and 40 batches of cupcakes
40 batches of cookies and 20 batches of cupcakes
30 batches of cookies and 30 batches of cupcakes
To find a reasonable solution, we need to consider the constraints given:
1. The baker’s budget is $400.
2. Each batch of cookies costs $2, and each batch of cupcakes costs $10.
3. The baker must make at least 20 more batches of cookies than cupcakes.
Let:
– ( c ) = batches of cookies
– ( u ) = batches of cupcakes
The cost equation can be written as:
[ 2c + 10u leq 400 ]
The relationship of batches is:
[ c geq u + 20 ]
Now, we can analyze each option:
1. 60 batches of cookies and 40 batches of cupcakes:
– Cost: ( 2(60) + 10(40) = 120 + 400 = 520 ) (exceeds budget)
– Batches relationship: ( 60 geq 40 + 20 ) (valid)
2. 20 batches of cookies and 40 batches of cupcakes:
– Cost: ( 2(20) + 10(40) = 40 + 400 = 440 ) (exceeds budget)
– Batches relationship: ( 20 geq 40 + 20 ) (invalid)
3. 40 batches of cookies and 20 batches of cupcakes:
– Cost: ( 2(40) + 10(20) =