Vince loads 10 boxes into his truck. some of the boxes weigh 20 pounds, and some weigh 30 pounds. the total weight of the boxes is 280 pounds. if x= the number of 20-pound boxes and y= the number of 30-pound boxes, which pair of equations will give the number of 20-pound and 30-pound boxes vince has?

Here, x represents the number of 20-pound boxes and y represents the number of 30 pound boxes.

As per the given condition: Vince loads 10 boxes into his truck.Some of the boxes weigh 20 pounds, and some weigh 30 pounds and the total weight of the boxes is 280 pounds.

⇒ x+ y =10                      .....[1]

and

20x+30y = 280               .....[2]

Multiply  equation [1]  by 20 we get;

Using distributive property:

20x + 20y = 200                   ....[3]

Subtract equation [3] from [2] we get;

Combine like terms;

10y = 80

Divide both sides by 10 we get;

y = 8

Substitute this y value in equation [1] we get;

x + 8 = 10

Subtract 8 from both sides we get;

x + 8 -8 =10-8

Simplify:

x = 2

Therefore, the pairs of equation are:  x+ y =10 and 20x+30y = 280

Vince has the number of 20-pound boxes is, 2 and the number of 30 pound boxes is, 8

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