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A delivery company operates 100 vehicles, consisting of cargo vans, delivery motorcycles, and box trucks in the proportions shown by the graph. Each cargo van can carry 3/2 as many packages per trip as each delivery motorcycle.
The company wants the ratio of the total number of packages that all cargo vans can carry per trip to the total number that all delivery motorcycles can carry per trip to be 5:6. The company will keep the total number of vehicles unchanged and will not change the number of box trucks or the carrying capacity of any vehicle.
Based on the information provided, select the option from each drop-down menu that creates the most accurate statement.
To achieve the desired ratio, the company could the number of cargo vans and the number of delivery motorcycles.
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22 Sep 2026, 01:30
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A delivery company operates 100 vehicles, consisting of cargo vans, delivery motorcycles, and box trucks in the proportions shown by the graph. Each cargo van can carry 3/2 as many packages per trip as each delivery motorcycle.
The company wants the ratio of the total number of packages that all cargo vans can carry per trip to the total number that all delivery motorcycles can carry per trip to be 5:6. The company will keep the total number of vehicles unchanged and will not change the number of box trucks or the carrying capacity of any vehicle.
Based on the information provided, select the option from each drop-down menu that creates the most accurate statement.
To achieve the desired ratio, the company could the number of cargo vans and the number of delivery motorcycles.
Official Solution:
From the graph, the company has:
Cargo vans: 20% of 100 = 20
Delivery motorcycles: 50% of 100 = 50
Box trucks: 30% of 100 = 30
Since each cargo van can carry 3/2 as many packages as each delivery motorcycle, let the carrying capacities of a cargo van and a motorcycle be 3 units and 2 units, respectively.
The current total carrying capacities are:
Cargo vans: 20 * 3 = 60
Delivery motorcycles: 50 * 2 = 100
Thus, the current ratio is:
60:100 = 3:5
The desired ratio is 5:6. Compared with 3:5, the cargo-van side needs to become larger relative to the motorcycle side.
Also, the total number of vehicles remains unchanged and the number of box trucks does not change. Therefore, any cargo vans added must be matched by the same number of motorcycles removed. So the number of cargo vans must increase, while the number of delivery motorcycles must decrease.
Let x be the number of motorcycles replaced by cargo vans.
Then there will be:
20 + x cargo vans
50 - x delivery motorcycles
The desired ratio is:
3(20 + x)/(2(50 - x)( = 5/6
18(20 + x) = 10(50 - x)
360 + 18x = 500 - 10x
28x = 140
x = 5
So the number of cargo vans increases from 20 to 25. The percentage increase is:
5/20 * 100% = 25%
The number of delivery motorcycles decreases from 50 to 45. The percentage decrease is:
5/50 * 100% = 10%
Therefore, the correct selections are increase by 25% and decrease by 10%.
Correct answer:
Drop-down 1: "increase by 25%"
Drop-down 2: "decrease by 10%"
General Discussion
15 Sep 2026, 09:13
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Let no of new cargo vans be x and motorcycle be y.
So, x + y = 70
And, 1.5x/y = 5/6
So, 9x = 5y
5x + 5y = 350
Substituting,
5x + 9x = 350
14x = 350
x = 25
therefore, y = 70 -25 = 45
So, cargo vans should be increased by 5/20 = 25%
And, motorcycles should be decreased by 5/50 = 10%
So, x + y = 70
And, 1.5x/y = 5/6
So, 9x = 5y
5x + 5y = 350
Substituting,
5x + 9x = 350
14x = 350
x = 25
therefore, y = 70 -25 = 45
So, cargo vans should be increased by 5/20 = 25%
And, motorcycles should be decreased by 5/50 = 10%
