An afternoon and an evening concert took place Saturday. Each afternoon ticket cost $15. Each evening ticket cost $20. A total of 450 tickets sold for both concerts totaling $8,000. How many afternoon concert tickets were sold?
Afternoon ticket=A
Evening ticket=B
A+B=450
15A+20B=8000
Solve the following system:
{A+B = 450 | (equation 1)
15 A+20 B = 8000 | (equation 2)
Swap equation 1 with equation 2:
{15 A+20 B = 8000 | (equation 1)
A+B = 450 | (equation 2)
Subtract 1/15 × (equation 1) from equation 2:
{15 A+20 B = 8000 | (equation 1)
0 A-B/3 = (-250)/3 | (equation 2)
Divide equation 1 by 5:
{3 A+4 B = 1600 | (equation 1)
0 A-B/3 = -250/3 | (equation 2)
Multiply equation 2 by -3:
{3 A+4 B = 1600 | (equation 1)
0 A+B = 250 | (equation 2)
Subtract 4 × (equation 2) from equation 1:
{3 A+0 B = 600 | (equation 1)
0 A+B = 250 | (equation 2)
Divide equation 1 by 3:
{A+0 B = 200 | (equation 1)
0 A+B = 250 | (equation 2)
Collect results:
Answer: | A = 200 and B=250
