Respuesta :
Hello!
1. Write an expression for the cost to buy and run this refrigerator for x years.
costs: $700
each year: $85
So, for x years, the expression will be:
[tex]f\mleft(x\mright)=85x+700[/tex]2. Write an expression for the total cost for the refrigerator over x years.
Let's do the same steps:
costs: $1000
each year: $25
So, for x years, we have:
[tex]g(x)=25x+1000[/tex]3. Over 10 years which refrigerator costs the most? By how much?
To solve this question, we just need to replace where is x by 10 in each of the functions, look:
First refrigerator:
[tex]\begin{gathered} f(x)=85x+700 \\ f(10)=(85\cdot10)+700 \\ f(10)=850+700 \\ f(10)=1550 \end{gathered}[/tex]Second refrigerator:
[tex]\begin{gathered} g(x)=25x+1000 \\ g(10)=(25\cdot10)+1000 \\ g(10)=250+1000 \\ g(10)=1250 \end{gathered}[/tex]So, the first refrigerator costs the most. The difference between the two refrigerators equals $300.
4. In how many years will the total costs for the two refrigerators be equal?
To find the value which equals the two functions, we just need to equal them, look:
[tex]\begin{gathered} 85x+700=25x+1000 \\ 85x-25x=1000-700 \\ 60x=300 \\ x=\frac{300}{60} \\ x=5 \end{gathered}[/tex]In five years the costs will be equal, let's prove it:
f(5) = g(5)
(85*5) +700 = (25*5) +1000
425 + 700 = 125 + 1000
1125 = 1125
