Question

Please show me how to solve using elimination: It takes a florist 3 h 15 min to make 3 small centerpieces and 3 large centerpieces. It takes 5 h 20 min to make 4 small center pieces and 7 large centerpieces. 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

3.25=combinedrate= 3S+3L
where S and L are the rates for each.

5.33=4S+7L

Now you have two equations.
5.33=4S+7L
3.25=3S+3L

ok, lets eliminate S.
multiply the top equation by 3, the bottom by 4
16=12S+21L
13=12S+12L
subtract the second equation from the first.
3=9L
L= 1/3 or rate is one large per hour
S=you figure it from either equation.