Chris stopped for gas twice on a long car trip. The price of gas at the first station was $1.45 per gallon, and the price of gas at the second station was $1.55 per gallon. On the trip, Chris bought a total of 20 gallons of gas and spent $29.80. Let x = the number of gallons that Chris bought at the first station and y = the number of gallons Chris bought at the second station.
Solve the system of equations to find the number of gallons that Chris bought at the second station.
a) 5
b) 8
c) 12
d) 20
2007-06-12 03:33:40 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1.45x + 1.55y = 29.8
x + y = 20
1.45(20-y) + 1.55y = 29.8
29 -1.45y +1.55y = 29.8
0.1y = 0.8
y = 8 (your answer is b)
x = 12
2007-06-12 03:40:19 · answer #1 · answered by gebobs 6 · 0⤊ 0⤋
x = number of gallons taken at first station
y = number of gallons taken at second station
x + y = 20
1.45*x + 1.55*y = 29.8
solving the two euations in the same way as we solve the intersection point of two lines
we obtain x and y
1.45*(x + y) = 20*1.45
=> 1.45*x + 1.45*y = 29
1.45*x + 1.55*y = 29.8
subtracting the above two equations
we get
0.1*y = 0.8
=> y = 8 gallons
x + y = 20
=> x + 8 =20
=> x = 12 gallons
therefore
no of gallons at first station = 8
number of gallons at second station = 12
therefore the anwer is 12
2007-06-12 10:43:54 · answer #2 · answered by vicky 2 · 1⤊ 0⤋
1.45x + 1.55y = 29.8 and x + y = 20
x = 20 - y and let us substitute that in the other equation.
1.45 (20 - y) + 1.55y = 29.8
29 - 1.45y + 1.55y = 29.8
0.1 y = 29.8 - 29 = 0.8
y = 0.8/0.1 = 8
Since y is 8 gallons, x will be 20 -8 = 12 gallons
Answer is b. 8 gallons
2007-06-12 10:52:29 · answer #3 · answered by Swamy 7 · 1⤊ 0⤋
1.45 x + 1.55 y = $29.80 equation 1
x + y =20 equation 2
solving the two equations
x=12
y = 8
answer is y = 8 gallon
2007-06-12 10:45:31 · answer #4 · answered by CPUcate 6 · 0⤊ 1⤋
b) 8
2007-06-12 12:13:46 · answer #5 · answered by Anonymous · 0⤊ 1⤋
b) 8
2007-06-12 10:38:37 · answer #6 · answered by raja 2 · 0⤊ 1⤋
x+y = 20
1.45x + 1.55y = 29.8
multiply top equation by 1.45
1.45x + 1.45y = 29
Subract equaquion 1 from equation 2
.1y = .8
y = 8
2007-06-12 10:40:37 · answer #7 · answered by Anonymous · 0⤊ 1⤋
how many gallons did he buy at the first station??
2007-06-12 10:46:25 · answer #8 · answered by leahsterlingmills 1 · 0⤊ 1⤋
1.45x + 1.55y = 29.80
x + y = 20
________________________________
x = 20 - y
1.45(20 - y) + 1.55 y = 29.80
29 - 1.45y + 1.55y = 29.80
29 + .10 y = 29.80
.10y = .80
y = 8
x + y = 20
x + 8 = 20
x = 12
Final Answer = 8
2007-06-12 10:44:43 · answer #9 · answered by Mike\ 3 · 0⤊ 1⤋
b
2007-06-12 10:38:16 · answer #10 · answered by Math Stud 3 · 0⤊ 1⤋