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Rose fills each of the rectangular regions of her rectangular flower

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Rose fills each of the rectangular regions of her rectangular flower  [#permalink]

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20 Mar 2019, 02:18
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Difficulty:

25% (medium)

Question Stats:

86% (03:07) correct 14% (03:36) wrong based on 35 sessions

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Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the figure. She plants one flower per square foot in each region. Asters cost \$1 each, begonias \$1.50 each, cannas \$2 each, dahlias \$2.50 each, and Easter lilies \$3 each. What is the least possible cost, in dollars, for her garden?

(A) 108
(B) 115
(C) 132
(D) 144
(E) 156

Attachment:

53688e514d1c6f1f99b771578717677d9fec99b3.png [ 3.96 KiB | Viewed 493 times ]

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Rose fills each of the rectangular regions of her rectangular flower  [#permalink]

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20 Mar 2019, 04:01
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Areas.png [ 10.29 KiB | Viewed 387 times ]

In order to make the least money, the area having maximum area must have the cheapest
flower. Since we are given the cost of the respective flowers(Asters cost \$1 each, begonias
\$1.50 each, cannas \$2 each, dahlias \$2.50 each, & Easter lilies \$3 each)

The largest area plot of 21 sq foot contains Asters, the second largest area plot of 20 sq food
contains begonnias, the third largest area of 15 sq foot contains cannas, the plot of 6 sq foot
contains dahlias, and the square part of 4 sq foot must contain Easter liles.

Therefore, the least cost for her garden is 21*1 + 20*1.5 + 15*2 + 6*2.5 + 4*3 = 108(Option A) square foot.
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Re: Rose fills each of the rectangular regions of her rectangular flower  [#permalink]

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20 Mar 2019, 06:34
Bunuel wrote:

Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the figure. She plants one flower per square foot in each region. Asters cost \$1 each, begonias \$1.50 each, cannas \$2 each, dahlias \$2.50 each, and Easter lilies \$3 each. What is the least possible cost, in dollars, for her garden?

(A) 108
(B) 115
(C) 132
(D) 144
(E) 156

Attachment:
53688e514d1c6f1f99b771578717677d9fec99b3.png

determine areas of all the given rectangular places
we get 21,20,15,6,4
multiply max area with lowest price flower
21*1+20*1.5+15*2+2.5*6+3*4 = 21+30+30+15+12 ;108
IMO A
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Re: Rose fills each of the rectangular regions of her rectangular flower  [#permalink]

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22 Mar 2019, 09:13
Bunuel wrote:

Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the figure. She plants one flower per square foot in each region. Asters cost \$1 each, begonias \$1.50 each, cannas \$2 each, dahlias \$2.50 each, and Easter lilies \$3 each. What is the least possible cost, in dollars, for her garden?

(A) 108
(B) 115
(C) 132
(D) 144
(E) 156

Attachment:
53688e514d1c6f1f99b771578717677d9fec99b3.png

Let’s determine the area of each region:

4 x 5 = 20

1 x 6 = 6

7 x 3 = 21

3 x 5 = 15

2 x 2 = 4 (This is the small region in the interior of the garden.)

So the least expensive way to plant the garden is to plant the cheapest flowers in the largest region, the next-cheapest flowers in the second largest region, and so forth. Thus, we have:

21 x 1 = \$21

20 x 1.5 = \$30

15 x 2 = \$30

6 x 2.5 = \$15

4 x 3 = \$12

Thus, the least possible cost is 21 + 30 + 30 + 15 + 12 = \$108.

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Re: Rose fills each of the rectangular regions of her rectangular flower   [#permalink] 22 Mar 2019, 09:13
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