Answer: [tex]\$4.34[/tex]
Step-by-step explanation:
We have the following information:
Fredburguer [tex]F[/tex], milkshake [tex]M[/tex] and an order of fries [tex]f[/tex] costs [tex]\$3.72[/tex]:
[tex]F+M+f=\$3.72[/tex] (1)
One Fredburguer is equal to a milkshake plus orders of fries:
[tex]F=M+2f[/tex] (2)
Three milshakes is equal to a Fredburguer plus an order of fries:
[tex]3M=F+f[/tex] (3)
And we are asked: If we have a Fredburguer, a milkshake and two orders of fries, how much do we have to pay?
[tex]F+M+2f=x[/tex] (4)
Well with the first three equations we have a system of equations to solve. Let's begin by isolating [tex]F[/tex] from (3):
[tex]F=3M-f[/tex] (5)
Making (2)=(5):
[tex]M+2f=3M-f[/tex] (6)
Isolating [tex]f[/tex]:
[tex]f=\frac{2}{3}M[/tex] (7)
Substituting (7) in (2):
[tex]F=M+2(\frac{2}{3}M)[/tex] (8)
Isolating [tex]F[/tex]:
[tex]F=\frac{7}{3}M[/tex] (9)
Substituting (7) and (9) in (1):
[tex]\frac{7}{3}M+M+\frac{2}{3}M=\$3.72[/tex] (10)
Isolating [tex]M[/tex]:
[tex]M=\$0.93[/tex] (11) This is the cost of a Milkshake
Substituting (11) in (7):
[tex]f=\frac{2}{3}\$0.93[/tex] (12)
[tex]f=\$0.62[/tex] (13) This is the cost of an order of frieds
Substituting (11) in (9):
[tex]F=\frac{7}{3}\$0.93[/tex] (14)
[tex]F=\$2.17[/tex] (15) This is the cost of a Fredburguer
Substituting (11), (13) and (15) in (4):
[tex]\$2.17+\$0.93+2(\$0.62)=x[/tex] (16)
Finally:
[tex]x=\$4.34[/tex] This is the cost of a Fredburguer, a milkshake and two orders of fries
