Answers:
Step-by-step explanation:
Our equation is: [tex]f=2.25+0.20(m-1)[/tex] With f meaning "fare" (price) and m meaning "miles".
Question 7 - Juan's fare for his ride costs $6.05. We must solve for [tex]m[/tex].
Step 1. Substitute - Substitute the fare for [tex]f[/tex] in the equation.
[tex]6.05=2.25+0.20(m-1)[/tex]
Step 2. Simplify/Solve - Solve for [tex]m[/tex].
[tex]6.05=2.25+0.20(m-1)[/tex]
- Distribute
[tex]6.05=2.25+0.2m-0.2[/tex]
- Subtract 0.2 from 2.25
[tex]6.05=2.05+0.2m[/tex]
- Subtract -2.05 from 6.05
[tex]4=0.2m[/tex]
- Divide both sides by 0.2
[tex]20=m[/tex]
And you have your answer of 20 miles.
Question 8 - Same equation, different fare.
Step 1. Substitute
[tex]7.65=2.25+0.20(m-1)[/tex]
Step 2. Solve
[tex]7.65=2.25+0.20(m-1)\\7.65=2.25+0.20m-0.20\\7.65=2.05+0.20m\\5.6=0.20m\\28=m[/tex]
And like so, we have [tex]m = 28[/tex]
The equation given is [tex]S=\frac{1}{5} (w-10e)[/tex]. S = typing speed, w = words per 5 mins, and e= errors.
Question 9 -
We are given this information: S = 55, W = 285. We are solving for e.
Substitute -
[tex]55=\frac{1}{5} (285 -10e)[/tex]
Solve -
[tex]55=\frac{1}{5} (285 -10e)\\55=\frac{1}{5} (285 -10e)\\55= 57-2e\\-2=-2e\\1=e[/tex]
So they would make 1 error.
Question 10 -
Information given: 300 = w, 5=e. We are solving for S
Substitute -
[tex]S= \frac{1}{5} (300-10(5))[/tex]
Solve -
[tex]S= \frac{1}{5} (300-10(5))\\S= \frac{1}{5} (300-50)\\S= \frac{1}{5} (300-50)\\S= \frac{1}{5} (250)\\S= 50[/tex]
Their speed is 50.
Question 11 -
Information given: S = 65, e = 4. We are solving for w.
Substitute -
[tex]65=\frac{1}{5} (w-10(4))[/tex]
Solve -
[tex]65=\frac{1}{5} (w-10(4))\\65=\frac{1}{5} (w-40)\\65=\frac{1}{5}w-8\\73=\frac{1}{5}w\\365=w[/tex]
So w = 365.
