The problem states: there are 9 more pencils than pens in a container. there are 25 writing utensils in the container in all. how many pens are there in the container?

let p represent the number of pens

which equation represents the situation?

a: 2(p+9)=25

b: 2p+9=25

c: 2p-9=25

d: p+9=25

The right answer is 2p + 9 = 25

According to this problem, we know:

The statement there are nine more pencils than pens in the container can be written as follows:

(1) P = p + 9

where:

P: Number of pencils

p: Number of pens

There are 25 writing utensils in the container in all, therefore:

(2) p + P = 25

Matching these two equations, we have:

(1) P = p + 9

(2) p + P = 25

Substituting (1) in (2):

p + (p+9) = 25

∴ 2p + 9 = 25

Therefore:

2p = 16 ∴ p = 8

and P

P = p + 9 ∴ P = 17

Finally:

There are 8 pens and 17 pencils in the container.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1