Respuesta :
Each text costs 5 cents more than each anytime minute.
Extra equations for you:
200x+400y=80
150x+350y=67.5
Answer : The true statement is, Each text message costs 5 cents more than each anytime minute.
Step-by-step explanation :
Let the anytime minutes be, x and text messages be, y.
As we are given that a month he used 200 anytime minutes and 400 text messages, and paid $80.00. The equation will be:
[tex]200x+400y=80.00[/tex] ...........(1)
[tex]x=\frac{80.00-400y}{200}[/tex] ............(A)
And,
As we are given that a month he used 150 anytime minutes and 350 text messages, and paid $67.50. The equation will be:
[tex]150x+350y=67.50[/tex] ...........(2)
Now solving these two equation by substitution method by putting equation A in equation 2, we get:
[tex]150x+350y=67.50[/tex]
[tex]150\times (\frac{80.00-400y}{200})+350y=67.50[/tex]
[tex]3\times (\frac{80.00-400y}{4})+350y=67.50[/tex]
[tex]\frac{240-1200y}{4}+350y=67.50[/tex]
[tex]240-1200y+1400y=270[/tex]
[tex]200y=30[/tex]
[tex]y=\frac{30}{200}[/tex]
[tex]y=\$ 0.15[/tex]
As we know that, $ 1 = 100 cents
So, $ 0.15 = 15 cents
y = 15 cents
Now put the value of 'y' in equation A, we get:
[tex]x=\frac{80.00-400y}{200}[/tex]
[tex]x=\frac{80.00-400(15)}{200}[/tex]
[tex]x=10[/tex]
x = 10 cents
As per given statements we conclude that, Each text message costs 5 cents more than each anytime minute is the correct statements.
Proof : [tex]y=5cents+x[/tex]
x = 10 cents
[tex]y=5cents+10cents=15cents[/tex]
Thus, the true statement is, Each text message costs 5 cents more than each anytime minute.
