Word Problems in 3 Variables Regs
Solve complex 3 variable systems of equations word problems!
In a jar there are 73 coins consisting of quarters, dimes, and pennies. There is $9.19. The number of quarters is 2 more than twice the number of dimes. How many quarters, pennies, and dimes are there? x+y+z=9.192+2z=y.10x+.25y+.01z=73 x+y+z=732+2z=zx+.05y+.5z=9.19 x+y+z=73.25x+.10y+.01z=9.192+2y=x .25x+.01z=9.192+2z=y.10x+.25y+.01z=73 Harlan High School Orchestra performed two concerts to raise money for a field trip. Tickets were $10 for adults (a) and $7 for students (s) and teachers (t). In total, 943 people attended both concerts, and the orchestra raised $7,435. The number of teachers who came was a forth of the number of students. Which of the following systems can be used to represent this situation? On the way home from school, a family enters the drive-through at a fast food restaurant.Mom: “I need 3 root beers, 2 junior burgers and one deluxe salad.”Clerk: “That will be $10.62. Please pull around.”Lucy: “Mom, I don’t want a burger. I’m a vegetarian now!”Mom: “OK—sorry. Can I get 3 root beers, 1 junior burger and 2 deluxe salads, instead?”Clerk: “No problem, ma’am. That brings your total to $11.22.”Mom: “Oh no. I’ve only got $11. Could you take off one of the root beers?”Clerk “Yes. Two root beers, 1 junior burger, and 2 salads. That’s $10.03.”What is the cost for each item individually? 3x+2y+z=10.623x+y+2z=11.222x+y+2z=10.03 x+3y+z=11.22x+y+z=10.03x+y+z=10.62 3x+2y+z=10.033x+y+2z=11.222x+y+2z=10.62 x+y+z=10.033x+2y+z=10.62x+y+3z=11.22 On a trip, Duke encounters some road construction that slows him down. While he is able to go 60 mph on the highway and 40 mph through cities, he can only go 20 mph past the construction. He spends one half the time on the highway as he does in construction, so this time the 380-mile trip takes 11 hours. How much of this time does he spend on the highway, in the city, and through road construction? 20x+40y+60z=11x+y+z=380.5z=x 40x+20y+60z=38060x+20y+40z=11.5x=z 60x+40y+20z=380x+y+z=11.5z=x x+y+z=380x+y+z=11.5x=z Marisa works at a candy shop. At the end of her shift, the change in the tip jar totals $10.65. The jar contains quarters (q), dimes (d), and nickels (n). The number of dimes is 4 more than twice the number of nickels and the number of quarters is 1 more than three times the number of nickels. Which system of equations could be used to find the number of dimes in the jar?