At the boxer carnival, you can exchange 45 tickets for various assortments of prizes. some of those assortments are below. how many tickets does it take to get a stuffed tiger?

1 goldfish, 5 tacky mirrors, 2 stuffed tiger

4 goldfish, 1 stuffed tiger

2 goldfish, 5 tacky mirrors

The stuffed tigger costs 25 tickets.

Step-by-step explanation:

Let's define G as the price of the goldfish, M as the price of the mirror and T as the price of the tigger.

1G + 5M + 2T = 45

4*G + 1T = 45

2G + 5M = 45

we want to know the value of T.

first, in the third equation we can isolate one of the variables, let's isolate G.

2G = 45 - 5M

G = (45 - 5M)/2

now, we can replace it in the other equations:

(45 - 5M)/2 + 5M + 2T = 45

4*(45 - 5M)/2 + 1T =45

now, we should isolate M in the second equation:

2(45 - 5M) = 45 - T

90 - 10M = 45 - T

M = -(45 - T + 90)/10

Now we can replace this in the other equation and finally solve it for T, but first simplify a bit the equation.

(45 - 5M)/2 + 5M + 2T = 45

45/2 - (5/2)M + 5M + 2T = 45

(5/2)M + 2T = 45 - 45/2 = 45/2

now we can multiplu every by 2 to remove the quotients:

5M + 4T = 45

now we can replace M

5*(-(45 - T + 90)/10)M + 4T = 45

((-45 + T - 90)/2 + 4T = 45

-135/2 + T/2 + 4T = 45

T*(4 + 1/2) = 45 + 135/2

T*4.5 = 45 + 135/2

T = (45 + 135/2)/4.5 = 25 tickets.

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)