2017 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 3 Easy

Tamara has three rows of two 6-feet by 2-feet flower beds in her garden. The beds are separated and also surrounded by 1-foot-wide walkways, as shown on the diagram. What is the total area of the walkways, in square feet? (2017 AMC 10A Problem, Question#3)

  • A.

    72

  • B.

    78

  • C.

    90

  • D.

    120

  • E.

    150

Answer:B

Finding the area of the shaded walkway can be achieved by computing the total area of Tamara's garden and then subtracting the combined area of her six flower beds.

Since the width of Tamara's garden contains three margins, the total width is 2\cdot6 + 3\cdot1= 15 feet.

Similarly, the height of Tamara's garden is 3\cdot2+4\cdot1=10 feet.

Therefore, the total area of the garden is 15\cdot10 = 150 square feet.

Finally, since the six flower beds each have an area of 2\cdot6 =12 square feet, the area we seek is 150-6\cdot12, and our answer is (\rm B) 78.

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