The owner of Rockport Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 8 small arrangements and 13 large arrangements, which took her a total of 123 minutes. After lunch, she arranged 10 small arrangements and 9 large arrangements, which took 103 minutes. How long does it take to assemble each type? The florist can assemble a small arrangement in minutes and a large one in minutes.
Let's denote the time it takes to assemble a small arrangement as x minutes and a large arrangement as y minutes.
From the information given, we can set up the following system of equations:
8x + 13y = 123
10x + 9y = 103
Now, we can solve these equations to find the values of x and y:
To solve this, we can multiply the second equation by 8 and the first equation by 10 to get rid of x:
80x + 72y = 824
80x + 104y = 984
Subtracting the first equation from the second equation gives us:
32y = 160
y = 5
Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
8x + 13(5) = 123
8x + 65 = 123
8x = 58
x = 7.25
Therefore, it takes 7.25 minutes to assemble a small arrangement and 5 minutes to assemble a large arrangement.