Question

The owner of Newberry Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 7 small arrangements and 3 large arrangements, which took her a total of 56 minutes. After lunch, she arranged 8 small arrangements and 2 large arrangements, which took 54 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.

Answer 1

By setting up a linear system of equations with the given times for assembling small and large arrangements, we find that it takes the florist 5 minutes to assemble a small arrangement and 7 minutes to assemble a large arrangement.

Step-by-step explanation:

The problem at hand is a linear system of equations where the total time taken to arrange flowers is given for different numbers of small and large arrangements. We can use variables to represent the time taken to assemble each type of arrangement. Let's define x to be the time to assemble a small arrangement and y to be the time to assemble a large arrangement.

For the morning session, the equation is:
7x + 3y = 56

For the afternoon session, the equation is:
8x + 2y = 54

Solving the system of equations

To solve this, we can use the method of substitution or elimination. Let's use elimination in this case.

Multiply the second equation by 1.5 to match the coefficient of y in the first equation:
12x + 3y = 81

Now subtract the first equation from this new equation:
(12x + 3y) - (7x + 3y) = 81 - 56
5x = 25
x = 5

Now we know it takes 5 minutes to assemble a small arrangement. Let's plug this value into one of the original equations to find y:

7(5) + 3y = 56
35 + 3y = 56
3y = 56 - 35
3y = 21
y = 7

So it takes 7 minutes to assemble a large arrangement.

The florist can assemble a small arrangement in 5 minutes and a large one in 7 minutes.