Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

Chapter 6 - Systems of Equations and Inequalities - Chapter Review - Page 410: 25

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.

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