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A cake shop sold only two types of cakes: regular cake, each is sold f
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19 Dec 2023, 05:58

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A cake shop sold only two types of cakes: regular cake, each is sold for $1 per cake, and premium cake, each is sold for $1.25 per cake. If r percent of the shop’s revenue from cake sales was from regular cake and if m percent of the cakes that the shop sold were regular cakes, which of the following expresses r in terms of m?

Indicate both the expressions.

A. \(\frac{4m}{5-\frac{m}{100}}\)

B. \(\frac{150m}{250-m}\)

C. \(\frac{300m}{500-2m}\)

D. \(\frac{500m}{625-m}\)

E. \(\frac{20m}{25-\frac{m}{25}}\)

Indicate both the expressions.

A. \(\frac{4m}{5-\frac{m}{100}}\)

B. \(\frac{150m}{250-m}\)

C. \(\frac{300m}{500-2m}\)

D. \(\frac{500m}{625-m}\)

E. \(\frac{20m}{25-\frac{m}{25}}\)

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Re: A cake shop sold only two types of cakes: regular cake, each is sold f
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13 Jan 2024, 06:25

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Re: A cake shop sold only two types of cakes: regular cake, each is sold f
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14 Feb 2024, 08:35

can someone elucidate this one

A cake shop sold only two types of cakes: regular cake, each is sold f
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17 Feb 2024, 11:44

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Let us consider the total number of cakes sold is 100 and out of them 20% are regular cakes

(m = 20%).

Thus, the number of regular cakes sold = 20% of 100 = 20

Revenue generated from sale of regular cakes = $ (1x 20) = $20

Number of premium cakes sold = 100 - 20 = 80

Revenue generated from sale of premium cakes = $ (1.25x 80) = $100

Thus total revenue = $(20+100)= $120

As r% of the total revenue comes from regular cakes, we have:

\(r=\frac{20}{120} *100 =16.6\)%

Now, let us substitute the value of m in the options and check which options give the result

16.6%

A. \(\dfrac{4m}{5-\frac{m}{100}}=\dfrac{4 * 20}{5-\frac{20}{100}}=\dfrac{80}{5-\frac{1}{5}}=\dfrac{400}{24}=16.6\) %

B. \(\dfrac{150m}{250-m}=\dfrac{150 * 20}{250-20}=\dfrac{300}{23} \neq 16.6\) %

C. \(\dfrac{300m}{500-2m}=\dfrac{300 * 20}{500-40}=\dfrac{600}{46} \neq 16.6\) %

D. \(\dfrac{400m}{500-m}=\dfrac{400 * 20}{500-20}=\dfrac{800}{48}= 16.6\) %

E. \(\dfrac{500m}{625-m}=\dfrac{500 * 20}{625-20}=\dfrac{1000}{605} \neq 16.6\) %

F. \(\dfrac{20p}{25-\frac{m}{25}}=\dfrac{20 * 20}{25-\frac{20}{25}}=\dfrac{400}{25-\frac{4}{5}}=\dfrac{2000}{121}\neq 16.6\) %

I hope this helps raghav4202

(m = 20%).

Thus, the number of regular cakes sold = 20% of 100 = 20

Revenue generated from sale of regular cakes = $ (1x 20) = $20

Number of premium cakes sold = 100 - 20 = 80

Revenue generated from sale of premium cakes = $ (1.25x 80) = $100

Thus total revenue = $(20+100)= $120

As r% of the total revenue comes from regular cakes, we have:

\(r=\frac{20}{120} *100 =16.6\)%

Now, let us substitute the value of m in the options and check which options give the result

16.6%

A. \(\dfrac{4m}{5-\frac{m}{100}}=\dfrac{4 * 20}{5-\frac{20}{100}}=\dfrac{80}{5-\frac{1}{5}}=\dfrac{400}{24}=16.6\) %

B. \(\dfrac{150m}{250-m}=\dfrac{150 * 20}{250-20}=\dfrac{300}{23} \neq 16.6\) %

C. \(\dfrac{300m}{500-2m}=\dfrac{300 * 20}{500-40}=\dfrac{600}{46} \neq 16.6\) %

D. \(\dfrac{400m}{500-m}=\dfrac{400 * 20}{500-20}=\dfrac{800}{48}= 16.6\) %

E. \(\dfrac{500m}{625-m}=\dfrac{500 * 20}{625-20}=\dfrac{1000}{605} \neq 16.6\) %

F. \(\dfrac{20p}{25-\frac{m}{25}}=\dfrac{20 * 20}{25-\frac{20}{25}}=\dfrac{400}{25-\frac{4}{5}}=\dfrac{2000}{121}\neq 16.6\) %

I hope this helps raghav4202

gmatclubot

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17 Feb 2024, 11:44
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