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Bonjour, j’ai un peu de mal à résoudre mon dm de maths section européenne.

Votre aide serait la bienvenue :

Exercise: Tara's favorite cereals are sold in two grocery stores in her neighbourhood: Tom's market and Gianni's grocery store. A usual pack of this brand of cereal contains 25 oz. of cereal and is sold $I.5.

A) Both stores decide to offer a special bargain on cereal. At Tom's market, the same pack of cereal is sold with 10% off. At Gianni's, the usual pack of cereal is replaced by a « special pack », that contains 10% more cereal. The « special pack » is sold for the same price.

1) How much does Tara pay for a pack of cereal at Tom's market?

2) Calculate the weight of cereal sold in a « special pack » at Gianni's.

3) Which store offers the best deal on cereal?

4) What if the usual pack of cereal was sold with 20% off at Tom's and the «special pack » sold at Gianni's contained 25% more cereal than the usual pack?

B) Assume that Tom's market sells a pack of cereal with a% off and that Gianni's grocery store sells a « special pack » of cereal containing b% more cereal for the same price of $1.5.

1) Which conditions do a and b require for both stores to sell this brand of cereal at the same price per ounce? 07

2) Explain why this equation doesn't have any economically sensible solution for

a = b.



Je n'arrive pas à voir la réponse, quelqu'un pourrait-il me répondre SVP

Répondre :

Réponse :

Explications étape par étape :

At Tom's market, Tara pays for a pack of cereal after a 10% discount. So, the price she pays is 90% of the original price:

0.90

×

1.5

=

$

1.35

0.90×1.5=$1.35

In Gianni's grocery store, the "special pack" contains 10% more cereal than the usual pack. Therefore, the weight of cereal in the special pack is

25

 

oz

+

0.10

×

25

 

oz

=

27.5

 

oz

25oz+0.10×25oz=27.5oz.

To compare the deals, let's calculate the price per ounce for each store:

At Tom's Market:

$

1.35

25

 

oz

=

$

0.054

/

25oz

$1.35

​

=$0.054/oz

At Gianni's Grocery Store:

$

1.5

27.5

 

oz

≈

$

0.0545

/

27.5oz

$1.5

​

≈$0.0545/oz

Since the price per ounce at Gianni's is slightly higher, Tom's Market offers the better deal.

Let's calculate the revised prices:

At Tom's Market with a 20% discount:

0.80

×

1.5

=

$

1.20

0.80×1.5=$1.20

At Gianni's Grocery Store with a "special pack" containing 25% more cereal:

25

 

oz

+

0.25

×

25

 

oz

=

31.25

 

oz

25oz+0.25×25oz=31.25oz

Now, let's compare the prices per ounce again:

At Tom's Market:

$

1.20

25

 

oz

=

$

0.048

/

25oz

$1.20

​

=$0.048/oz

At Gianni's Grocery Store:

$

1.5

31.25

 

oz

≈

$

0.048

/

31.25oz

$1.5

​

≈$0.048/oz

Since both stores offer the same price per ounce now, the deal is equal.

B)

For both stores to sell the cereal at the same price per ounce:

1.5

25

=

1.5

25

+

100

×

25

×

(

1

−

100

)

25

1.5

​

=

25+

100

b

​

×25

1.5

​

×(1−

100

a

​

)

This equation ensures that the price per ounce is the same for both deals.

When

=

a=b, the equation becomes:

1.5

25

=

1.5

25

+

100

×

25

×

(

1

−

100

)

25

1.5

​

=

25+

100

a

​

×25

1.5

​

×(1−

100

a

​

)

This equation is not economically sensible because it implies that both stores are offering the same discount and the same increase in quantity, which contradicts the idea of competition and differentiation between products in a market. It wouldn't make sense for both stores to offer identical deals.

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