Answer:
The difference in per-mile costs for the two companies is $0.12
Step-by-step explanation:
Gabi sets up the equation [tex]0.22m+7.20=0.1m+8.40[/tex] to find out after how many miles, m, the companies will charge the same amount.
The first company charges [tex]c_1=0.22m+7.20[/tex] for m miles driven.
The second company charges [tex]c_2=0.1m+8.40[/tex] for m miles driven.
In both these functions, numbers 7.20 and 8,40 represent the initial fee the companies charge.
Numbers 0.22 and 0.1 represent per-mile costs.
Thus, the difference in per-mile costs is [tex]0.22-0.1=0.12[/tex]
Another way to solve this problem is to find the cost per mile driven for each company:
1. Cost per-mile 1st company
[tex]c_1(0)=0.22\cdot 0+7.20=7.20\\ \\c_1(1)=0.22\cdot 1+7.20=7.42\\ \\c_1(1)-c_1(0)-7.42-7.20=0.22[/tex]
2. Cost per-mile 2nd company
[tex]c_2(0)=0.1\cdot 0+8.40=8.40\\ \\c_2(1)=0.1\cdot 1+8.40=8.50\\ \\c_2(1)-c_2(0)=8.50-8.40=0.1[/tex]
3. Difference:
[tex]0.22-0.1=0.12[/tex]
