Question

At work one day, Erica Franz received 18 packages, Speedy Delivery delivered three times as many as Ralph's Express, while Ralph's Express delivered two more than Send Quick Package Service. How many packages did each service deliver to Erica?

Answer 1

By setting up equations and solving them, we found out that Send Quick Package Service delivered 2 packages, Ralph's Express delivered 4 packages, and Speedy Delivery delivered 12 packages to Erica.

Step-by-step explanation:

To solve the problem of how many packages each delivery service delivered to Erica, we can set up some equations based on the given information:

• Speedy Delivery delivered three times as many packages as Ralph's Express.
• Ralph's Express delivered two more packages than Send Quick Package Service.
• The total number of packages delivered by all three services is 18.

Let's define some variables:

• Let x represent the number of packages Send Quick Package Service delivered.
• Therefore, Ralph's Express delivered x + 2 packages.
• And Speedy Delivery delivered 3(x + 2) packages.

The equation representing the total number of packages is:

x + (x + 2) + 3(x + 2) = 18

Solving this equation, we combine like terms:

x + x + 2 + 3x + 6 = 18

Which simplifies to:

5x + 8 = 18

Subtracting 8 from both sides gives:

5x = 10

Dividing by 5,

x = 2

Thus, Send Quick Package Service delivered 2 packages, Ralph's Express delivered 4 packages (2 + 2), and Speedy Delivery delivered 12 packages (3(2 + 2)).