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Step2247 [10]
3 years ago
5

Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day. At the same rates two Nissans, four Fords, and thr

ee Chevrolets cost $107 per day, whereas four Nissans, three Fords, and two Chevrolets cost $102 per day. Find the rental rate for the Fords.
Mathematics
1 answer:
Sindrei [870]3 years ago
3 0

Answer:

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

Step-by-step 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 = \frac{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 = \frac{324}{27}

y = 12

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

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