Question

Group of up to 40 people are going on a trip to Washington, DC. Some will travel

a van that holds 12 people, and the rest will buy train tickets. Write an inequality
hat can be used to find the number of train tickets that the group will need.

Answer 1

y <= 40

Explanation:

Let's call the number of people traveling by van "x", and the number of people buying train tickets "y". We know that the total number of people in the group is 40, so we can write the equation:

x + y = 40

And we also know that the van can hold up to 12 people, so we can write the inequality:

0 <= x <= 12

Now, to find the number of train tickets, we just need to substitute

x = 40 - y into the second inequality:

0 <= 40 - y <= 12

Expanding and solving for y, we get:

0 <= 40 - y <= 12

-40 <= -y <= -28

y >= 28

y <= 40

So the number of train tickets needed (y) is equal to or greater than 28 and equal to or less than 40.

Answer 2

Inequality: 12 + x ≤ 40

Solution: x ≤ 28

Explanation:

Let x be the number of train tickets that the group will need.

As the van holds 12 people and the rest will buy train tickets, an expression for the total number of people is:

• 12 + x

If the group is up to 40 people then 12 + x will be less than or equal to 40:

• 12 + x ≤ 40

Therefore, the inequality that can be used to find the number of train tickets that the group will need is:

• 12 + x ≤ 40

To solve the inequality, subtract 12 from both sides:

⇒ 12 + x - 12 ≤ 40 - 12

⇒ x ≤ 28

Therefore the number of train tickets that the group will need is less than or equal to 28 tickets.