Question

Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day. At the same rates two Nissans, four Fords, and three Chevrolets cost $107 per day, whereas four Nissans, three Fords, and two Chevrolets cost $102 per day. Find the rental rate for the Fords.

Answer 1

The rental rate for the Fords is of $12 per day.

Explanation:

This question is solved using a system of equations.

I am going to say that:

x is the cost of a Nissan.

y is the cost of a Ford.

z is the cost of a Chevrolet.

Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day.

This means that:

`3x + 2y + 4z = 106`

Two Nissans, four Fords, and three Chevrolets cost $107 per day

This means that:

`2x + 4y + 3z = 107`

Four Nissans, three Fords, and two Chevrolets cost $102 per day.

This means that:

`4x + 3y + 2z = 102`

From the first equation:

`4z = 106 - 3x - 2y`

`2z = 53 - 1.5x - y`

`z = 26.5 - 0.75x - 0.5y`

Replacing into the third equation:

`4x + 3y + 53 - 1.5x - y = 102`

`2.5x + 2y = 49`

From the second equation:

`2x + 4y + 3z = 107`

`2x = 107 - 4y - 3z`

`x = 53.5 - 2y - 1.5z`

`x = 53.5 - 2y - 1.5(26.5 - 0.75x - 0.5y)`

`x - 1.125x = 53.5 - 2y - 39.75 + 0.75y`

`-0.125x = 13.75 - 1.25y`

`0.125x = 1.25y - 13.75`

`x = (1.25y - 13.75)/(0.125)`

`x = 10y - 110`

Find the rental rate for the Fords.

We have to find y, so:

`2.5x + 2y = 49`

`2.5(10y - 110) + 2y = 49`

`25y - 275 + 2y = 49`

`27y = 324`

`y = (324)/(27)`

`y = 12`

The rental rate for the Fords is of $12 per day.