IMAT 2018 Q15 [Lawn Mowing]

Mr and Mrs Massa’s rectangular lawn measures 10 metres by 6 metres. They pay Giovanni to cut the grass and trim the edges. Giovanni charges a fixed rate per square metre of grass to be cut and another fixed rate per metre of edge to be trimmed. For Mr and Mrs Massa’s lawn, this results in a charge of $12 to cut the grass and $8 to trim the edges.

Now, Mr and Mrs Costa next door want Giovanni to do the same for them. Their lawn is also rectangular and measures 15 metres by 9 metres.

If he charges them at the same rate as the Massas, how much will Giovanni charge Mr and Mrs Costa, in total, for cutting their grass and trimming their edges?

A. $35
B. $30
C. $45
D. $39
E. $36


Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
  • Eliminate any non-essential information
  • Draw a picture, graph, or equation
  • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve.

What do we know:

  • Mr and Mrs Massa’s lawn size: 10 meters by 6 meters
  • He charged them \$12 to cut the grass and \$8 to trim the edges
  • He will charge Mr and Mrs Costa the same rate
  • Mr and Mrs Costa have a rectangular lawn that is 15 meters by 9 meters

First, let’s find the perimeter and area of each lawn:

Mr and Mrs Massa

Area: (10m)(6m) = 60m^2

Perimeter: 10m + 10m + 6m + 6m = 32m

Mr and Mrs Costa
Area: (15m)(9m) = 135m^2
(break it down if you need to: (9)(10)+(9)(5) = 90 + 45 = 135)

Perimeter: 15m + 15m + 9m + 9m = 30m + 18m = 48m
Now we can find out what the ratios are between the two different lawns.

Now to find the costs:
If Giovanni charged \$12 to cut the lawn, which was 60m^2, we can find out the m^2 per dollar.
60m^2/\$12 = 5m^2/\$1

Now for the perimeter:
32m/\$8 = 4m^2/\$1

Now we just need to apply these costs to Mr and Mrs Costa’s lawn.

(135m^2)/(5m^2/\$1) = \$27

(48m)/(4m^2/\$1) = \$12

Total cost = \$27 + \$12 = \$39

\fcolorbox{red}{grey!30}{Therefore the answer is D, $\$39.$}

Note: If you think it is weird to use m^2/dollar, think of the numbers given to us. To out the cost per square meter would be much more laborious, and we still end with the same result. You could also solve this question with ratios, but the problem is that the area ratio is 12:27, which is difficult to work with. This exam is about speed and efficiency, so do not be afraid to take the simplest way in terms of numbers instead of what is typical if the answer is the same.

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