Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a flight had 52 passengers who paid a total of $1360, how many first class passengers were there on the trip?
+118724 Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a flight had 52 passengers who paid a total of $1360, how many first class passengers were there on the trip?
F+T=52
30F+25T=1360
Now solve them simultaneously. Can you do that?
+118724 Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a flight had 52 passengers who paid a total of $1360, how many first class passengers were there on the trip?
F+T=52
30F+25T=1360
Now solve them simultaneously. Can you do that?
Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a flight had 52 passengers who paid a total of $1360, how many first class passengers were there on the trip?
Let the number of first class=F
Let the number of tourist class=T, then we have:
F + T=52, But,
30F + 25T=1360
Solve the following system:
{30 F+25 T = 1360 | (equation 1)
F+T = 52 | (equation 2)
Subtract 1/30 × (equation 1) from equation 2:
{30 F+25 T = 1360 | (equation 1)
0 F+T/6 = 20/3 | (equation 2)
Divide equation 1 by 5:
{6 F+5 T = 272 | (equation 1)
0 F+T/6 = 20/3 | (equation 2)
Multiply equation 2 by 6:
{6 F+5 T = 272 | (equation 1)
0 F+T = 40 | (equation 2)
Subtract 5 × (equation 2) from equation 1:
{6 F+0 T = 72 | (equation 1)
0 F+T = 40 | (equation 2)
Divide equation 1 by 6:
{F+0 T = 12 | (equation 1)
0 F+T = 40 | (equation 2)
Collect results:
Answer: | F = 12 and T = 40
