Respuesta :
Answer:
The cost of one hot dog can't be determine from the given condition
Step-by-step explanation:
From the question,
Total cost of four hot dogs and three bags of candy is $14.37 and twelve hot dogs and nine bags of candy is $24.74.
So,
Let the number of hot dog be x
and the number of bags of candy be y.
According to question,
Equations formed by given statement are,
[tex]4{x} + 3{y} = 14.37[/tex] .................(1)
[tex]12{x} + 9{y} = 24.74[/tex] .................(2)
Here, these are the linear equation in two variables says x & y.
[tex]a1=4[/tex] [tex]b1=3[/tex] [tex]c1=14.37[/tex]
[tex]a2=12[/tex] [tex]b2=9[/tex] [tex]c1=24.74[/tex]
When ,
[tex]\frac{a1}{a2}[/tex] ≠ [tex]\frac{b1}{b2}[/tex] = [tex]\frac{c1}{c2}[/tex] gives Unique solution.
[tex]\frac{a1}{a2}[/tex] = [tex]\frac{b1}{b2}[/tex] = [tex]\frac{c1}{c2}[/tex] gives Infinite many solutions.
[tex]\frac{a1}{a2}[/tex] = [tex]\frac{b1}{b2}[/tex] ≠ [tex]\frac{c1}{c2}[/tex] gives No solution.
From Equation (1) & (2) we get ,
[tex]\frac{4}{12}[/tex] = [tex]\frac{3}{9}[/tex] ≠ [tex]\frac{14.37}{24.37}[/tex]
This condition says that the given equation have no solution.
Hence the cost of one hot dog can't be determine from the given condition.
The system of equations have infinite number of solutions
Let the price of one hot dog be x
Let the price of each candy be y
If four hot dogs and three bags of candy cost $14.37, then;
4x + 3y = 14.37 ................. 1
Similarly, if Twelve hot dogs and nine bags of candy cost $24.74, then;
12x + 9y = 24.74 .............2
Solve both equations simultaneously;
4x + 3y = 14.37 ................. 1 * 3
12x + 9y = 24.74 .............2 * 1
_________________________________
12x + 9y = 43.11
12x + 9y = 24.74
Subtract both equations
0x + 0y = 43.11 - 24.74
0y = 18.37
y = 18.37/0
y = ∞
This shows that the system of equations have an infinite number of solutions
Learn more here: https://brainly.com/question/15165519
