Answer
Small centerpieces take 25 minutes
Large centerpieces take 40 minutes.
Work Step by Step
Use the information given to make two equations:3y+3x=3$\frac{1}{4}$ and 4y+7x=6 $\frac{1}{3}$.Y represents the small centerpiece and X represents the large centerpiece. Multiply the first equation by -4 and the second by 3 to be able to eliminate the Y-variable:
-4(3y+3x=3$\frac{1}{4}$)=-12y-12x=-13
3(4y+7x=6 $\frac{1}{3}$)=12y+21x=19
Combine the equations:
-12y-12x=-13
12y+21x=19
9x=6 -divide both sides by 9-
x=2/3(40 minutes)
Plug in x=2/3 into one of the equations:
3y+3(2/3)=3$\frac{1}{4}$
3y+2=3$\frac{1}{4}$
3y=1$\frac{1}{4}$
y=$\frac{5}{12}$(25 minutes)
The small centerpiece takes 25 minutes and the large centerpiece takes 40 minutes.
