Question

A truck can be rented from Company A for ​$70 a day plus ​$0.70 per mile. Company B charges ​$20 a day plus ​$0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same. At nothing ​miles, the rental costs are the same from either company.

Answer 1

Let no of miles be y

• A=0.7y+70
• B=0.8y+20

`\\ \sf\longmapsto A=B`

`\\ \sf\longmapsto 0.7y+70=0.8y+20`

`\\ \sf\longmapsto 0.8y-0.7y=70-20`

`\\ \sf\longmapsto 0.1y=50`

`\\ \sf\longmapsto y=(50)/(0.1)`

`\\ \sf\longmapsto y=500miles`

Answer 2

• 500 miles

Explanation:

Let the number of miles is x.

Then for each company we have total charge of:

• A = 0.7x + 70
• B = 0.8x + 20

Since A = B, solve for x:

• 0.7x + 70 = 0.8x + 20
• 0.8x - 0.7x = 70 - 20
• 0.1x = 50
• x = 50/0.1
• x = 500 miles