Problem

3. To surf the internet for 15 minutes at an airport, it costs $\$ 4.05$. For 40 minutes, it costs $\$ 5.80$. Write and solve a linear equation to find the cost for surfing the web for one hour.
14. Water boils at $100^{\circ}$ Celsius or $212^{\circ}$ Fahrenheit. Water freezes at $0^{\circ}$ Celsius or $32^{\circ}$ Fahrenheit. If the weather forecaster says it will be $25^{\circ}$ Celsius today, write and solve a linear equation to find what Fahrenheit temperature this is.

Answer

Expert–verified
Hide Steps
Answer

\(\boxed{f = 77^\circ}\)

Steps

Step 1 :Let's denote the cost for surfing the internet for \(x\) minutes as \(C(x)\).

Step 2 :We know that \(C(15) = \$4.05\) and \(C(40) = \$5.80\).

Step 3 :We can write the equation of the line passing through the points \((15, 4.05)\) and \((40, 5.80)\).

Step 4 :The slope of the line is \(\frac{5.80 - 4.05}{40 - 15} = \frac{1.75}{25} = \$0.07\) per minute.

Step 5 :So, the equation of the line is \(C(x) = 0.07x + b\).

Step 6 :To find \(b\), we can substitute one of the points into the equation. Let's use \((15, 4.05)\):

Step 7 :\(4.05 = 0.07 \cdot 15 + b\),

Step 8 :\(b = 4.05 - 0.07 \cdot 15 = \$2.95\).

Step 9 :So, the cost for surfing the internet for \(x\) minutes is \(C(x) = 0.07x + 2.95\).

Step 10 :To find the cost for surfing the web for one hour (or 60 minutes), we substitute \(x = 60\) into the equation:

Step 11 :\(C(60) = 0.07 \cdot 60 + 2.95\)

Step 12 :\(\boxed{C(60) = \$7.15}\)

Step 13 :We know that \(f=32+1.8c\).

Step 14 :To find the Fahrenheit temperature when it is \(25^\circ\) Celsius, we substitute \(c = 25\) into the equation:

Step 15 :\(f =32+1.8c\)

Step 16 :\(f =32+1.8(25)\)

Step 17 :\(\boxed{f = 77^\circ}\)

link_gpt