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melomori [17]
3 years ago
6

casey has a small business making dessert baskets. she estimates that her fixed weekly costs for rent, electricity, and salaries

are $200. the ingredients for one dessert basket cost $2.50. casey’s total costs for last week were $500. how many dessert baskets did she make?
Mathematics
1 answer:
m_a_m_a [10]3 years ago
3 0
500 = 200 + 2.50x
x = amount of dessert baskets

500 - 200 = 300.
300 = 2.50x
300 ÷ 2.50 = 120.
Casey made 120 dessert baskets.
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By applying the knowledge of similar triangles, the lengths of AE and AB are:

a. \mathbf{AE = 3.9 $ cm}\\\\

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<em>See the image in the attachment for the referred diagram.</em>

<em />

  • The two triangles, triangle AEC and triangle BDC are similar triangles.
  • Therefore, the ratio of the corresponding sides of triangles AEC and BDC will be the same.

<em>This implies that</em>:

  • AC/BC = EC/DC = AE/DB

<em><u>Given:</u></em>

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<u>a. </u><u>Find the length of </u><u>AE</u><u>:</u>

EC/DC = AE/DB

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\frac{8.1}{5.4} = \frac{AE}{2.6}

  • Cross multiply

5.4 \times AE = 8.1 \times 2.6\\\\5.4 \times AE = 21.06

  • Divide both sides by 5.4

AE = \frac{21.06}{5.4} = 3.9 $ cm

<u>b. </u><u>Find the length of </u><u>AB:</u>

AB = AC - BC

AC = 6.15 cm

To find BC, use AC/BC = EC/DC.

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\frac{6.15}{BC} = \frac{8.1}{5.4}

  • Cross multiply

BC \times 8.1 = 6.15 \times 5.4\\\\BC = \frac{6.15 \times 5.4}{8.1} \\\\BC = 4.1

  • Thus:

AB = AC - BC

  • Substitute

AB = 6.15 - 4.1\\\\AB = 2.05 $ cm

Therefore, by applying the knowledge of similar triangles, the lengths of AE and AB are:

a. \mathbf{AE = 3.9 $ cm}\\\\

b. \mathbf{AB = 2.05 $ cm} \\\\

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