Question

systems of linear equations word problems: medium
paulos economics course requires two papers—one long and one short—throughout the semester. the number of pages, l, in the long paper is 1 more than 2 times the number of pages, s, in the short paper. if the total number of pages for both papers is 40, how many pages must be in the long paper?
show calculator
how do i enter a student - produced response on the sat? show me!

Explanation:

Step1: Set up equations

Let $l$ be the number of pages in the long - paper and $s$ be the number of pages in the short - paper. We have the equations: $l = 2s+1$ (the number of pages in the long paper is 1 more than 2 times the number of pages in the short paper) and $l + s=40$ (the total number of pages for both papers is 40).

Step2: Substitute the first equation into the second

Substitute $l = 2s + 1$ into $l + s=40$. We get $(2s + 1)+s=40$.
Combining like terms: $2s+1 + s=40$ simplifies to $3s+1 = 40$.
Subtract 1 from both sides: $3s=40 - 1=39$.
Divide both sides by 3: $s=\frac{39}{3}=13$.

Step3: Find the number of pages in the long paper

Substitute $s = 13$ into the equation $l = 2s+1$. Then $l=2\times13 + 1=26 + 1=27$.

Answer:

27