Question

This morning, she assembled 2 small arrangements and 5 large arrangements, which took her a total of 60 minutes. After lunch, she arranged 5 small arrangements and 1 large arrangement, which took 35 minutes. How long does it take to assemble each type?

Answer 1

To determine how long it takes to assemble each type, use a system of equations. It takes 5 minutes to assemble a small arrangement and 10 minutes to assemble a large arrangement.

Step-by-step explanation:

To determine how long it takes to assemble each type, we need to set up a system of equations. 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 given information, we can write the following equations:

2s + 5l = 60

5s + l = 35

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

From the second equation, we can isolate 'l' as follows: l = 35 - 5s

Substitute this value of 'l' into the first equation:

2s + 5(35 - 5s) = 60

Simplify and solve for 's': 2s + 175 - 25s = 60, -23s + 175 = 60, -23s = -115, s = 5

Now substitute the value of 's' back into either of the original equations to find 'l'. Using the second equation:

5(5) + l = 35, 25 + l = 35, l = 10

Therefore, it takes 5 minutes to assemble a small arrangement and 10 minutes to assemble a large arrangement.