Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.The owner of Riverside Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 4 small arrangements and 3 large arrangements, which took her a total of 26 minutes. After lunch, she arranged 4 small arrangements and 5 large arrangements, which took 38 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.Submit
Question
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.The owner of Riverside Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 4 small arrangements and 3 large arrangements, which took her a total of 26 minutes. After lunch, she arranged 4 small arrangements and 5 large arrangements, which took 38 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.Submit
Solution
Let's denote the time it takes to assemble a small arrangement as S and the time it takes to assemble a large arrangement as L.
From the problem, we can write two equations:
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4S + 3L = 26 (This represents the time it took to assemble 4 small and 3 large arrangements in the morning)
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4S + 5L = 38 (This represents the time it took to assemble 4 small and 5 large arrangements after lunch)
To solve this system of equations using elimination, we can subtract the first equation from the second to eliminate S:
(4S + 5L) - (4S + 3L) = 38 - 26 2L = 12 L = 12 / 2 L = 6 minutes
Substitute L = 6 into the first equation:
4S + 3*6 = 26 4S + 18 = 26 4S = 26 - 18 4S = 8 S = 8 / 4 S = 2 minutes
So, the florist can assemble a small arrangement in 2 minutes and a large one in 6 minutes.
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