Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

A bride-to-be had already finished assembling 15 wedding favors when the maid of honor came into the room to help. The bride assembles at a rate of 1 favor per minute. In contrast, the maid of honor works at a speed of 2 favors per minute. Eventually, they will both have assembled the same number of favors. How many favors will each have made? How long will that take?


The bride-to-be and her maid of honor will each have made how many
favors in how many minutes.

Answer 1

Let \( b \) represent the number of favors assembled by the bride and \( m \) represent the number of favors assembled by the maid of honor.

We know that:
- The bride-to-be has already assembled 15 favors.
- The bride assembles favors at a rate of 1 favor per minute.
- The maid of honor assembles favors at a rate of 2 favors per minute.

Let \( t \) represent the time in minutes that they work together.

The equations for the number of favors assembled can be written as:
- For the bride:
\[
b = 15 + 1t
\]
- For the maid of honor:
\[
m = 2t
\]

They will have assembled the same number of favors when \( b = m \). Therefore, we can set the two equations equal to each other:
\[
15 + t = 2t
\]

Now, solve for \( t \):
\[
15 + t = 2t
\]
\[
15 = 2t - t
\]
\[
15 = t
\]

So, they will work together for 15 minutes.

Now, we can determine how many favors each has assembled:
1. For the bride:
\[
b = 15 + 1(15) = 15 + 15 = 30
\]
2. For the maid of honor:
\[
m = 2(15) = 30
\]

Thus, the bride-to-be and her maid of honor will each have made **30 favors** in **15 minutes**.

**Fill in the blanks:**

The bride-to-be and her maid of honor will each have made **30** favors in **15** minutes.