The ratio of the number of cars to the number of SUVs in a parking lot is 4:1. The ratio of the number SUVs to the number of Minivans is 4:5. (A) Find the ratio of the number of minivans in the parking lot. (B) if there are 20 minivans, how many vehicles are there all together?
Please help me understand thanks.
To find the ratio of the number of minivans in the parking lot, we need to find the common ratio between the number of SUVs and minivans.
Given that the ratio of SUVs to minivans is 4:5, we can set up the equation 4x = 5, where x represents the common ratio.
Solving for x, we divide both sides of the equation by 4: x = 5/4.
So, the ratio of the number of minivans in the parking lot is 5/4.
To find the total number of vehicles in the parking lot, we need to add up the number of cars, SUVs, and minivans.
Let's say the number of SUVs is represented by y. Since the ratio of cars to SUVs is 4:1, the number of cars would be 4y.
Now, we know that the ratio of SUVs to minivans is 4:5. Since the total ratio of SUVs and minivans is 4 + 5 = 9, we can set up the equation y/(5/4) = 9.
Simplifying this equation, we multiply both sides by 5/4: y = 9 * (5/4).
Solving for y, we find that y = 45/4.
Therefore, the total number of SUVs in the parking lot is 45/4.
Given that there are 20 minivans, we can substitute this value into the equation y = 45/4 to find the value of y:
45/4 = 20/(5/4).
Simplifying this equation, we multiply both sides by 5/4: 45 * (5/4) = 20.
Multiplying out both sides, we find that 225/4 = 20.
To find the total number of vehicles, we sum the number of cars, SUVs, and minivans:
Total number of vehicles = 4y (number of cars) + y (number of SUVs) + 20 (number of minivans).
Substituting in the values we found earlier, we have:
Total number of vehicles = 4 * (45/4) + (45/4) + 20.
Simplifying this equation, we find that the total number of vehicles is 45 + 45 + 20 = 110.
Therefore, there are 110 vehicles in total in the parking lot.
To find the ratio of the number of minivans in the parking lot, we need to consider the information given about the ratios of cars to SUVs and SUVs to minivans.
Let's assign variables to the number of cars, SUVs, and minivans. Let C represent the number of cars, S represent the number of SUVs, and M represent the number of minivans.
From the information given, the ratio of cars to SUVs is 4:1. This means that for every 4 cars, there is 1 SUV. So we can write the equation: C/S = 4/1.
The ratio of SUVs to minivans is 4:5. This means that for every 4 SUVs, there are 5 minivans. So we can write the equation: S/M = 4/5.
(A) To find the ratio of minivans, we need to solve for M in the equation S/M = 4/5:
S/M = 4/5
5S = 4M
M/S = 5/4
This tells us that the ratio of minivans in the parking lot is 5:4. So the answer to part (A) is 5:4.
(B) If there are 20 minivans, we can use the ratio in part (A) to find the total number of vehicles in the parking lot.
The ratio of minivans is 5:4, which means that for every 5 parts of minivans, there are 4 parts of the total number of vehicles.
Let's assign V as the total number of vehicles. So we have the equation: M/V = 5/4.
If there are 20 minivans, we can substitute M = 20 into the equation above:
20/V = 5/4
To solve for V, we can cross-multiply:
20 * 4 = 5 * V
80 = 5V
V = 80/5
V = 16
Therefore, if there are 20 minivans, there are a total of 16 vehicles in the parking lot.
cars : SUV's = 4:1 = 16:4
SUV's : Minivans = 4:5
now that I have a common "4" for the SUV's in both, I can say
cars : SUV's : minivans = 16 : 4 : 5
or
= 16x : 4x : 5x
but 5x = 20
x = 4
so we have 64 cars, 16 SUV's , and 20 minivans for a total of 100 vehicles
check:
cars: SUV's = 64:16 = 4 : 1
SUV's : minivans = 16 : 20 = 4 : 5
My answer is correct