Questions: A bride-to-be had already finished assembling 18 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 favors in minutes.

A bride-to-be had already finished assembling 18 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 favors in minutes.

Transcript text: A bride-to-be had already finished assembling 18 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 $\square$ favors in $\square$ minutes.

Solution

Solution Steps

Step 1: Determine the Time Until Equal Favors Assembled

Let $ t $ be the time in minutes after the maid of honor starts helping. The equation for the number of favors assembled by both the bride and the maid of honor is given by:

\[ 18 + 1t = 2t \]

Solving for $ t $:

\[ t = 36 \text{ minutes} \]

Step 2: Calculate the Number of Favors Assembled

Now, we can calculate the total number of favors each will have assembled after $ t $ minutes.

For the bride:

\[ \text{Bride's favors} = 18 + 1 \cdot 36 = 54 \]

For the maid of honor:

\[ \text{Maid's favors} = 2 \cdot 36 = 72 \]