Two groups of students order burritos and tacos at a local restaurant. One order of 3 burritoes and 4 tacos costs $11.33. The other order of 9 burritos and 5 tacos costs $23.56.
a. Write a system of equations that describes this situation.
b. Solve by elimination to find the cost of a burrito and the cost of a taco.
2007-09-15 12:07:11 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
It's simultaneous equations
3b+4t=11.33
9b+5t=23.56
2007-09-15 12:12:16 · answer #1 · answered by Tom P 6 · 0⤊ 0⤋
Let b= # of burritos bought
t = # of tacos bought
To get a system of equations, use the relationships between burritos, tacos, and dollars.
The cost of 3 burritos and 4 tacos is $11.33
The cost of 9 burritos and 5 tacos is $ 23.56
3b + 4t = 11.33
9b + 5t = 23.56
This is the system of equations.
Multiply both sides of the 1st equation by -3.
(3b + 4t = 11.33) -3
9b + 5t = 23.56
This will eliminate the b variable.
-9b - 12t = -33.99
9b + 5t = 23.56
Add them together and get:
0b -7t = -10.43
See how the b's cancel out?
-7t = -10.43
Divide both sides by -7
t = 1.49
The cost of a taco is $1.49.
Plug this in to one of the original equations and get:
3b + 4(1.49) = 11.33
3b + 5.96 = 11.33
3b = 5.37
b = 1.79
The cost of a burrito is $1.79
2007-09-15 19:18:40 · answer #2 · answered by Q_142857 3 · 0⤊ 0⤋
3b+4t=11.33, 9b+5t=23.56 Multiply the first equation by 3 and subtract from second equation:
9b+ 5t=23.56
-[9b+12t=33.99]
-7t= -10.43 => t=1.49 => b=[11.33-4*1.49]/3
b=1.79
Tacos are $1.49 each
Burritos are $1.79 each
2007-09-15 19:23:49 · answer #3 · answered by oldschool 7 · 0⤊ 0⤋
Let
x=burritos
y=tacos
then
3x+4y=1133 and
9x+5y=2356
Now solve it.
Doug
2007-09-15 19:13:39 · answer #4 · answered by doug_donaghue 7 · 0⤊ 0⤋