A school store must spend no more than $225 for an order of pens and pencils. Each pen costs $0.75, and each pencil costs $0.25. This relationship is shown in the graph. The store needs at least 100 more pencils than pens. Which choice is a reasonable solution

To determine which choice is reasonable, we can set up the constraints based on the information provided:

1. Cost Constraint:

– Let ( p ) represent the number of pens and ( c ) represent the number of pencils.

– The cost equation is:

[

0.75p + 0.25c leq 225

]

2. Pencil Constraint:

– The store needs at least 100 more pencils than pens, which can be expressed as:

[

c geq p + 100

]

Now, let’s analyze the provided options:

1. 300 pens and 900 pencils:

– Cost: ( 0.75(300) + 0.25(900) = 225 + 225 = 450 ) (exceeds budget)

2. 300 pens and 200 pencils:

– Cost: ( 0.75(300) + 0.25(200) = 225 + 50 = 275 ) (exceeds budget)

3. 200 pens and 300 pencils:

– Cost: ( 0.75(200) + 0.25(300) = 150 + 75 = 225 ) (fits budget)

– Pencil constraint: ( 300 geq 200 + 100 ) (