Please explain in detail how to solve the following problem using elimination: It takes a florist 3 h 15 min to make 3 small centerpieces and 3 large centerpieces. It takes

Question

6h 20 min to make 4 small centerpieces and 7 large center pieces. How long does it take to make each small centerpiece and each large centerpiece? Write and solve a system of equations to find your answer.

Answer 1

changing all time values to minutes to avoid fractions,

3S + 3L = 195
4S + 7L = 380

In order to eliminate S or L, we need to manipulate the equations, while not invalidating them.

So, multiply the first by 4 and the second by 3 to get an S coefficient of 12 for both equations:

12S + 12L = 780
12S + 21L = 1140

Now subtract one from the other, and the S's vanish:

9L = 360
L = 40

Now substitute L into either of the two original equations to get

S = 25

So, it takes 25 min. to make a small centerpiece, and 40 min. to make a large one.