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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.