At an auto dealership, \frac{2}{5} of the vehicles in the inventory are sedans, 35\% are S… — ACT

At an auto dealership, $\frac{2}{5}$ of the vehicles in the inventory are sedans, $35\%$ are SUVs, and the remaining 45 vehicles are trucks. What is the total number of vehicles in the dealership's inventory?

Cevap: 180 vehicles

Cevap

The total number of vehicles in the dealership's inventory is 180.

Converting

\frac{2}{5}

to a percentage yields

40\%

. Adding the

40\%

sedans and

35\%

SUVs shows that

75\%

of the inventory consists of sedans and SUVs. Consequently, the remaining

25\%

of the inventory consists of trucks. Since there are 45 trucks,

25\%

of the total inventory equals 45. Dividing 45 by

0.25

yields the total inventory of 180 vehicles.

Adım Adım Çözüm

Convert fraction of sedans to a percentage

Sedans represent

40\%

of the total inventory.

To combine the amounts easily, convert

\frac{2}{5}

to percentage form:

\frac{2}{5} = 0.40 = 40\%

Calculate the combined percentage of sedans and SUVs

Sedans and SUVs together make up

75\%

of the inventory.

Add the two percentages:

40\% + 35\% = 75\%

Determine the remaining percentage representing trucks

Trucks make up

25\%

of the inventory.

The entire inventory equals

100\%

, so

100\% - 75\% = 25\%

Solve for the total number of vehicles

The total inventory is 180 vehicles.

Set up the equation

25\% \text{ of Total} = 45

, which gives

0.25 \times \text{Total} = 45

, so

\text{Total} = \frac{45}{0.25} = 180

Anahtar Kavram

Converting fractions to percentages to find an unknown total quantity from a remaining part

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