Question

The owner of Rockport Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 11 small arrangements and 1 large arrangement, which took her a total of 62 minutes. After lunch, she arranged 12 small arrangements and 1 large arrangement, which took 67 minutes. How long does it take to assemble each type?

Answer 1

To solve this, we need to write a system of equations.

We know that it took her 62 minutes to assemble 11 small and 1 large.

Let's call the small arrangements S, and the large L.

Then:

$11S+L=62$

After lunch, she did 12 small and 1 large in 67 minutes. Then:

$12S+L=67$

Now we have the system of equations:

$\begin{cases}11S+L=62 \\ 12S+L=67\end{cases}$

To solve by elimination, we need to eliminate one unknown by adding or substracting the two equations. If we rest the first equation to the second equation:

$(12S+L)-(11S+L)=67-62$

Now we can solve:

$\begin{gathered} 12S-11S+L-L=65-62 \\ S=5 \end{gathered}$

To make a small arrangement takes her 5 minutes. Now we can go back to the first equation and replace S = 5:

$\begin{cases}11S+L=62 \\ S=5\end{cases}\Rightarrow11\cdot5+L=62$

And solve for L:

$\begin{gathered} 55+L=62 \\ L=62-55 \\ L=7 \end{gathered}$

Then it takes her 7 minutes to make a large arrangement.