Answer: Adult tickets cost 27 dollars while Child tickets cost 16 dollars
Step-by-step explanation: The question clearly states that adult tickets and child tickets are sold for a combined total sales amount. However the combination of adult and child tickets always yield a different sales total depending on the mix of tickets. This implies that both tickets have different amounts attached to them.
For a start, we shall assign an alphabet to each of the unknown ticket values. Let’s assume that adult tickets are represented by letter A, and child tickets are represented by B. If 4 adult and 3 child tickets are sold for 156 dollars, then what we have is
4A + 3B = 156 —————(1)
Also if 3 adult tickets and 4 child tickets are sold for 145 dollars, then what we have here is
3A + 4B = 145 ————-(2)
Now we have a pair of simultaneous equations which are;
4A + 3B = 156 —————(1)
3A + 4B = 145 —————(2)
We shall apply the elimination method to solve for A and B. First of all we shall eliminate the coefficients of A by multiplying equation (1) with 3, and multiplying equation (2) with 4. This now gives us
12A + 9B = 468 ———-(3)
12A + 16B = 580 ———(4)
Subtract equation 3 from equation 4 and we arrive at
7B = 112
(Note that 12A - 12A = 0)
Divide both sides of the equation by 7
B = 16
Having that in mind, we shall now substitute for the value of B = 16 in equation 1.
4A + 3B = 156
4A + 3(16) = 156
4A + 48 = 156
Subtract 48 from both sides of the equation
4A = 108
Divide both sides of the equation by 4
A = 27
Hence, adult tickets are sold for 27 dollars while child tickets are sold for 16 dollars.