A car showroom had 10y cars, 20y motorcycles and 18 vans. In a particular month, 4y cars , 3y motorcycles and 15 vans were sold.
a.) Find the total number of wheels on the remaining vehicles in terms of x.
b.) If y=21, how many wheels were there?
An indoor stadium has 25 460 seats. 25% of them are Category A seats. For a concert, Mr Ramly requires 40% of the seats to be Catergory A seats. Find the increase in the number if Category A seats.
a)
(10y-4y)*4 + (20y-3y)*2 + (18-15)*4
= 24y+34y+12
= 58y + 12 wheels remaining
b) 58*21+12 = 1230
an extra 15% of seating is needed.
15% of 25460 = 3819
a) To find the total number of wheels on the remaining vehicles in terms of x, we need to calculate the number of wheels on each type of vehicle and then subtract the number of vehicles sold.
Number of wheels per car: 4
Number of wheels per motorcycle: 2
Number of wheels per van: 4
Total number of wheels before sales:
10y cars * 4 (wheels per car) +
20y motorcycles * 2 (wheels per motorcycle) +
18 vans * 4 (wheels per van)
After sales:
Remaining cars: 10y cars - 4y cars
Remaining motorcycles: 20y motorcycles - 3y motorcycles
Remaining vans: 18 vans - 15 vans
Total number of wheels after sales:
(10y cars - 4y cars) * 4 (wheels per car) +
(20y motorcycles - 3y motorcycles) * 2 (wheels per motorcycle) +
(18 vans - 15 vans) * 4 (wheels per van)
So, the total number of wheels on the remaining vehicles in terms of x is:
4 * (10y - 4y) + 2 * (20y - 3y) + 4 * (18 - 15)
b) If y = 21, we can substitute y = 21 into the equation from part a) to find the total number of wheels in that case:
Total number of wheels = 4 * (10 * 21 - 4 * 21) + 2 * (20 * 21 - 3 * 21) + 4 * (18 - 15)
Simplifying the equation, we get:
Total number of wheels = 4 * (210 - 84) + 2 * (420 - 63) + 4 * 3
Total number of wheels = 4 * 126 + 2 * 357 + 12
Total number of wheels = 504 + 714 + 12
Total number of wheels = 1230
So if y = 21, there are 1230 wheels in total.
a) To find the total number of wheels on the remaining vehicles, we need to first calculate the number of vehicles of each type that are left after the sales.
Cars remaining = 10y - 4y
Motorcycles remaining = 20y - 3y
Vans remaining = 18 - 15
Now, we need to calculate the number of wheels on each type of vehicle. Cars and motorcycles have 4 wheels each, while vans have 4 wheels each.
Total number of wheels on remaining cars = (Cars remaining) * 4
Total number of wheels on remaining motorcycles = (Motorcycles remaining) * 4
Total number of wheels on remaining vans = (Vans remaining) * 4
To find the total number of wheels on the remaining vehicles, we add up the number of wheels from each type of vehicle.
Total number of wheels on the remaining vehicles = Total number of wheels on remaining cars + Total number of wheels on remaining motorcycles + Total number of wheels on remaining vans
Therefore, in terms of x, the total number of wheels on the remaining vehicles is:
(10y - 4y) * 4 + (20y - 3y) * 4 + (18 - 15) * 4
Simplifying further,
= 6y * 4 + 17y * 4 + 3 * 4
= 24y + 68y + 12
= 92y + 12
b) If y = 21, to find the total number of wheels, we substitute the value of y into the expression we obtained in part a.
Total number of wheels = 92y + 12
Substituting y = 21,
Total number of wheels = 92(21) + 12
= 1932 + 12
= 1944
Thus, if y = 21, there would be a total of 1944 wheels.