Two dump trucks have capacities of 10 tons and 12 tons. They make a total of 20 round trips to haul 226 tons of topsoil for a landscaping project. How many round trips does each truck make?

Answers (1)

2021-02-10

Let x= truck
Actually, x is the number of round trips made by the 10 ton truck and y is the number of round trips made by the 12 ton truck.
x + y = 20
We know from the problem that if you add together the number of round trips made by each truck, you get the 20 trip total.
x= 20-y
This is just math to isolate x. So, now we can substitute "20-y" for x in the equation and it will be easier to solve.
10 (20-y) + 12y = 226
This equation reflects how much topsoil each truck carried. Truck x (which is '20-y' now) carried 10 tons on each of its round trips, and truck y carried 12 tons per trip. [Note that even though it's a round trip, they only carried soil in one direction.]
200-10y + 12y = 226
This step and the ones that follow are just math steps to simplify the equation. This one turns 10(20-y) into 200 - 10y
2(100-5y+6y)=226
This is one way to further simplify by pulling 2 out from each part of the left hand side.
2(100+y) = 226
This is just showing that -5y + 6y is the same as 1y or just y
100 + y = 113
y= 13
x = 7

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