Destiny has $47 to spend at the fair. The entrance fee to the fair is $5, and the rides cost $7 each. How many rides can Destiny go on to spend exactly $47?

Question

Let r be the number of rides Destiny goes on. Start by writing an expression that represents the total amount of money she spends.
Nice!
Complete the equation to represent the amount of money Destiny has to spend at the fair.
7r+5 =
Excellent!
Solve for the value of r. Solve on paper, or show your work below. Then enter your answer on Zearn.
7r+5
=
47

r
=
You got it!
What does your answer of 6 mean in this situation?
7r+5 = 47
r = 6

Destiny needs to spend $6 on rides to spend $47.

Destiny can go to the fair for 6 hours to spend $47.

Destiny can ride 6 rides to spend $47.
Good work!
Let’s say that Destiny wants to have some money left over after the fair. Complete the statement to write an inequality that represents Destiny having money left over after going to the fair.
7r+5 = 47
r = 6

7r+5 47

Answer 1

To represent the situation where Destiny wants to have some money left over after going to the fair, we can modify the equation into an inequality. The original equation is:

\[ 7r + 5 = 47 \]

To show that she spends less than her total amount of $47, we change the equal sign to a less than sign:

\[ 7r + 5 < 47 \]

This means we want the total amount Destiny spends (which is made up of the rides and the entrance fee) to be less than $47.

Now, let's simplify the inequality:

1. Subtract 5 from both sides:

\[ 7r < 47 - 5 \]

2. Which simplifies to:

\[ 7r < 42 \]

3. Now, divide both sides by 7:

\[ r < 6 \]

So the final inequality representing the scenario where Destiny has money left over after going to the fair is:

\[ 7r + 5 < 47 \]

or equivalently,

\[ r < 6 \]

This means that Destiny can go on at most 5 rides if she wants to have some money left over after spending at the fair.