A theater sold 4 adult tickets and 3 child tickets for 156 dollars they also sold 3 adult tickets and 4 child tickets for 145 dollars. How much are adult and child tickets

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.

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4