At an auto dealership, 52 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?
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Cevap: 180
Cevap
The total number of vehicles in the dealership's inventory is 180.
Converting 52 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
1
Convert fraction of sedans to a percentage
Sedans represent 40% of the total inventory.
To combine the amounts easily, convert 52 to percentage form: 52=0.40=40%.
2
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%.
3
Determine the remaining percentage representing trucks
Trucks make up 25% of the inventory.
The entire inventory equals 100%, so 100%−75%=25%.
4
Solve for the total number of vehicles
The total inventory is 180 vehicles.
Set up the equation 25% of Total=45, which gives 0.25×Total=45, so Total=0.2545=180.
Anahtar Kavram
Converting fractions to percentages to find an unknown total quantity from a remaining part