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Zorluk: ZorLinear Equations in One Variable

A commercial drone delivery service charges a flat rate of 15.5015.50 dollars per delivery plus a fuel surcharge of 1.801.80 dollars per mile. During a promotional event, the service offers a 20%20\% discount off the fuel surcharge only. If the total cost for a specific delivery during this promotion was 27.0227.02 dollars, how many miles did the drone travel for this delivery?

Cevap: 8 miles

Cevap

8
The correct answer is 8. The promotional fuel surcharge is reduced by 20%20\% from the normal 1.801.80 dollars per mile, resulting in a rate of 1.80×(1−0.20)=1.441.80 \times (1 - 0.20) = 1.44 dollars per mile. The linear equation modeling the total cost for a delivery of mm miles during the promotion is 15.50+1.44m=27.0215.50 + 1.44m = 27.02. Subtracting 15.5015.50 from both sides gives 1.44m=11.521.44m = 11.52. Dividing both sides by 1.441.44 yields the distance m=8m = 8 miles.

Adım Adım Çözüm

1
Determine the discounted fuel surcharge per mile.
The discounted surcharge is 1.441.44 dollars per mile.
A 20%20\% discount is applied to the original 1.801.80 dollars per mile fuel surcharge: 1.80×(1−0.20)=1.441.80 \times (1 - 0.20) = 1.44.
2
Set up the linear equation representing the total promotional cost.
15.50+1.44m=27.0215.50 + 1.44m = 27.02, where mm represents the number of miles traveled.
The total cost is the sum of the flat rate of 15.5015.50 dollars and the promotional fuel surcharge of 1.441.44 dollars per mile multiplied by the number of miles.
3
Subtract the flat rate from both sides of the equation.
1.44m=11.521.44m = 11.52
To isolate the term with the variable mm, subtract the flat rate of 15.5015.50 from the total promotional cost of 27.0227.02.
4
Solve for the distance by division.
m=8m = 8
Divide both sides of the equation by the promotional rate per mile, 1.441.44, to find the number of miles.

Anahtar Kavram

Formulating and solving a multi-step linear equation in one variable with decimals and percentages to represent a real-world scenario.
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Konular

Linear Equations in One Variable

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