Question

At work one​ day, Erica Franz received 33 packages. Speedy Delivery delivered four times as many as​ Ralph's Express, while​ Ralph's Express delivered three more than SendQuick Package Service. How many packages did each service deliver to​ Erica?

Answer 1

Let's define the number of packages delivered by each service as follows:

- Let \( x \) be the number of packages delivered by SendQuick Package Service.
- Then, Ralph's Express delivered \( x + 3 \) packages (since Ralph's Express delivered three more than SendQuick).
- Speedy Delivery delivered \( 4(x + 3) \) packages (since Speedy Delivery delivered four times as many as Ralph's Express).

According to the problem, the total number of packages delivered is 33. Therefore, we can set up the following equation:

\[
x + (x + 3) + 4(x + 3) = 33
\]

Now, let's simplify and solve the equation:

1. Combine like terms:
\[
x + x + 3 + 4(x + 3) = 33
\]
\[
2x + 3 + 4x + 12 = 33
\]
\[
6x + 15 = 33
\]

2. Subtract 15 from both sides:
\[
6x = 33 - 15
\]
\[
6x = 18
\]

3. Divide by 6:
\[
x = 3
\]

Now that we have \( x \), we can find the number of packages delivered by each service:

- SendQuick Package Service: \( x = 3 \)
- Ralph's Express: \( x + 3 = 3 + 3 = 6 \)
- Speedy Delivery: \( 4(x + 3) = 4 \times 6 = 24 \)

In summary, the number of packages delivered by each service is:
- SendQuick Package Service: **3 packages**
- Ralph's Express: **6 packages**
- Speedy Delivery: **24 packages**