SOLUTION: This exercise is solving applied problems: three equations. Sally works at Starbucks a 10-oz cup of coffee costs \$1.09, a 14-oz cup costs \$1.29 and a 20-oz cup costs \$1.49.

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: This exercise is solving applied problems: three equations. Sally works at Starbucks a 10-oz cup of coffee costs \$1.09, a 14-oz cup costs \$1.29 and a 20-oz cup costs \$1.49.       Log On

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 Click here to see ALL problems on Mixture Word Problems Question 34579: This exercise is solving applied problems: three equations. Sally works at Starbucks a 10-oz cup of coffee costs \$1.09, a 14-oz cup costs \$1.29 and a 20-oz cup costs \$1.49. During a busy period, Sally served 34 cups of coffee, emptying five 96-oz pots while collecting \$43.46. How many cups of each size did Sally fill? I know the answer is 8 10-oz, 20 14-oz, and 6 20-oz but how do you get those answers?Answer by Paul(988)   (Show Source): You can put this solution on YOUR website!Let the 10-oz cup be x Let the 14-oz cup be y Let the 20-oz cup be z Now we know that: x+y+z=34 (equation 1) "emptying five 96-oz pots..." translate that into 5 of 96-oz pots so 10x+14y+20z=5(96) (equation 2) 109x+129y+149z=4346 (equation 3) Mutliply equation 1 by 14: and subbtract 2 by 1: 10x+14y+20z=480 14x+14y+14z=476 -4x+6z=4 (equation 4) Subbtract equation 2 by equation 3 And mutliply equation 2 by 129 and equation 3 by 14 1290x+1806y+2580z=61920 1526x+1806y+2086z=60844 -236x+494z=1076 (equation 5) Multiply equation 4 by 236 and subbstract E5 by E4 -236x+494z=1076 -236x+354z=236 140z=840 z=6 ```-4x+6(6)=4 -4x=-32 x=8 In x+y+z=34 8+y+6=34 y=20 Hence, their are 8 10-oz cups, 20 14-oz cups and 6 20-oz cups. Paul. ```