Question

. Suppose a refrigerator that sells for $700 costs $85 a year for electricity. Write an expression for the cost to buy and run this refrigerator for x years. 2. Suppose another refrigerator costs $1000 and $25 a year for electricity. Write an expression for the total cost for the refrigerator over x years. 3. Over 10 years which refrigerator costs the most? By how much? 4. In how many years will the total costs for the two refrigerators be equal?

Answer 1

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:

`f\mleft(x\mright)=85x+700`

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:

`g(x)=25x+1000`

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:

`\begin{gathered} f(x)=85x+700 \\ f(10)=(85\cdot10)+700 \\ f(10)=850+700 \\ f(10)=1550 \end{gathered}`

Second refrigerator:

`\begin{gathered} g(x)=25x+1000 \\ g(10)=(25\cdot10)+1000 \\ g(10)=250+1000 \\ g(10)=1250 \end{gathered}`

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:

`\begin{gathered} 85x+700=25x+1000 \\ 85x-25x=1000-700 \\ 60x=300 \\ x=(300)/(60) \\ x=5 \end{gathered}`

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