Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks 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 inminutes and a large one in minutes .
Let x be the time it takes to assemble a small arrangement
Let y be the time it takes to assemble a large arrangement
The system of equations is:
8x + 13y = 123
10x + 9y = 103
Using elimination method:
-16x - 26y = -246 (Multiply the first equation by -2)
20x + 18y = 206 (Multiply the second equation by 2)
Adding the two equations together:
4x - 8y = -40
x - 2y = -10
x = 2y - 10
Substitute x = 2y - 10 into one of the original equations:
8(2y - 10) + 13y = 123
16y - 80 + 13y = 123
29y = 203
y = 7
Substitute y = 7 into x = 2y - 10:
x = 2(7) - 10
x = 4
Therefore, it takes 4 minutes to assemble a small arrangement and 7 minutes to assemble a large arrangement.