Ricky is building a ramp for his family's corner store to make it easier to receive deliveries. He wants to make the ramp 3 ft wide and 6 ft long. If the boards are 6 in wide, how many linear feet of lumber will he need?

9 linear feet of lumber will be needed.

Step-by-step explanation:

Since the ramp is going to be 3 ft wide and 6 ft long and we have 6 in wide boards, we are going to be stacking the boards side by side to cover the length and width of the ramp.

Let n boards cover the width of the ramp, then number of boards × width of one board = width of ramp.

So, n × 6 in = 3 ft

Since 12 in = 1 ft, we have

n × 6 in = 3 ft = 3 × 1 ft = 3 × 12 in

n × 6 in = 36 in

n = 36 in/6 in

n = 6

Let n' boards cover the length of the ramp, then number of boards × width of one board = length of ramp.

So, n' × 6 in = 6 ft

Since 12 in = 1 ft, we have

n' × 6 in = 6 ft = 6 × 1 ft = 6 × 12 in

n' × 6 in = 72 in

n' = 72 in/6 in

n' = 12

Thus, the total number of boards needed is n" = n + n' = 6 + 12 = 18

So, the number of inches of board needed is thus n" × width of one board = 18 × 6 in = 108 in

Now, since 12 in = 1 ft, 1 in = 1/12 ft

108 in = 108 × 1/12 ft = 108/12 ft = 9 ft

So, 9 linear feet of lumber will be needed.

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