College Algebra

Question

Find the augmented matrix of the corresponding linear system.

a) Volunteers X,Y, and Z offered to stuff 864 envelopes with newspaper for a charity. Volunteer X could assemble 170 per hour, volunteer Y, 121 per hour, and volunteer Z, 146 per hour. They worked a total of 6 hours. The sum of the number of hours that volunteers Y and Z spent was twice what volunteer X spent. How long did each of them work?

b) Ron attends a cocktail party. He wants to limit his food intake to 133 g protein, 120 g fat, and 165 g carbohydrate. According to the health conscious hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, and 6 g carbohydrate. How many of each snack can he eat to obtain his goal?

Answer 1

1/170 +1/121 + 1/146 = 1/h

= (121(146) + (170)(146) + 121(170)/(170)(121)(146) = 1/6 = 1/h

then h=6 hours when they work together

= (17666+ 24820+ 20570)/3003220

= (42486 +20,570)/3,003,220

= 63,056/3,003,220

= about .020996 which doesn't = 1/6 = .1666...

closer to h = 48 hours when working all together

at 6 hours each X does 6x170

Y does 6x121, Z 6x146

for a total 1020 + 726 + 876 = 1746+ 876

= 2622 envelopes stuffed

with hours worked the same 48 for X, Y and Z

but it's given that

Y + Z's hours worked = twice X's hours worked

which could mean hours worked were the same 48 for each

but it's given they only worked 6 hours

that's 6 hours for X 6 for Y 6 for Z as 6+6 = 2(6) = 12