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Sagot :
To determine the correct expression for the total amount Max spent at the bakery, we need to calculate the cost of each type of item he bought and then sum these costs.
1. Cost of donuts: Max bought [tex]\( x \)[/tex] donuts, and each donut costs [tex]\( \$ 1.09 \)[/tex]. Therefore, the total cost of the donuts is:
[tex]\[ 1.09x \][/tex]
2. Cost of cinnamon bagels: Max bought [tex]\( y \)[/tex] cinnamon bagels, and each cinnamon bagel costs [tex]\( \$ 1.59 \)[/tex]. Therefore, the total cost of the cinnamon bagels is:
[tex]\[ 1.59y \][/tex]
3. Cost of onion bagels: Max bought [tex]\( z \)[/tex] onion bagels, and each onion bagel costs [tex]\( \$ 1.59 \)[/tex] (the same price as the cinnamon bagels). Therefore, the total cost of the onion bagels is:
[tex]\[ 1.59z \][/tex]
To find the total amount Max spent at the bakery, we sum the costs of the donuts, cinnamon bagels, and onion bagels:
[tex]\[ 1.09x + 1.59y + 1.59z \][/tex]
Let’s analyze the options to see which one corresponds to this expression:
A. [tex]\( 1.09 x + 1.59 y z \)[/tex]
- This option is incorrect because [tex]\( 1.59 yz \)[/tex] implies a multiplication between [tex]\( y \)[/tex] and [tex]\( z \)[/tex], which is not the correct way to add up costs.
B. [tex]\( 1.09 x + 1.59 y + 1.59 z \)[/tex]
- This option is correct. It correctly adds the costs of the donuts, cinnamon bagels, and onion bagels: [tex]\( 1.09x + 1.59y + 1.59z \)[/tex].
C. [tex]\( 1.09 x + 3.18 (y + z) \)[/tex]
- This option is incorrect because it incorrectly multiplies the sum [tex]\( y + z \)[/tex] by [tex]\( 3.18 \)[/tex], but each [tex]\( y \)[/tex] and [tex]\( z \)[/tex] item should be multiplied by [tex]\( 1.59 \)[/tex] individually.
D. [tex]\( (1.09 + 1.59)(x + y + z) \)[/tex]
- This option is incorrect because it adds the costs [tex]\( 1.09 \)[/tex] and [tex]\( 1.59 \)[/tex] together and then multiplies the sum by the total number of items [tex]\( x + y + z \)[/tex], which does not correctly reflect the separate pricing structure.
Therefore, the expression that correctly represents the total amount Max spent at the bakery is:
[tex]\[ \boxed{1.09 x + 1.59 y + 1.59 z} \][/tex]
The correct answer is option [tex]\( \text{B} \)[/tex].
1. Cost of donuts: Max bought [tex]\( x \)[/tex] donuts, and each donut costs [tex]\( \$ 1.09 \)[/tex]. Therefore, the total cost of the donuts is:
[tex]\[ 1.09x \][/tex]
2. Cost of cinnamon bagels: Max bought [tex]\( y \)[/tex] cinnamon bagels, and each cinnamon bagel costs [tex]\( \$ 1.59 \)[/tex]. Therefore, the total cost of the cinnamon bagels is:
[tex]\[ 1.59y \][/tex]
3. Cost of onion bagels: Max bought [tex]\( z \)[/tex] onion bagels, and each onion bagel costs [tex]\( \$ 1.59 \)[/tex] (the same price as the cinnamon bagels). Therefore, the total cost of the onion bagels is:
[tex]\[ 1.59z \][/tex]
To find the total amount Max spent at the bakery, we sum the costs of the donuts, cinnamon bagels, and onion bagels:
[tex]\[ 1.09x + 1.59y + 1.59z \][/tex]
Let’s analyze the options to see which one corresponds to this expression:
A. [tex]\( 1.09 x + 1.59 y z \)[/tex]
- This option is incorrect because [tex]\( 1.59 yz \)[/tex] implies a multiplication between [tex]\( y \)[/tex] and [tex]\( z \)[/tex], which is not the correct way to add up costs.
B. [tex]\( 1.09 x + 1.59 y + 1.59 z \)[/tex]
- This option is correct. It correctly adds the costs of the donuts, cinnamon bagels, and onion bagels: [tex]\( 1.09x + 1.59y + 1.59z \)[/tex].
C. [tex]\( 1.09 x + 3.18 (y + z) \)[/tex]
- This option is incorrect because it incorrectly multiplies the sum [tex]\( y + z \)[/tex] by [tex]\( 3.18 \)[/tex], but each [tex]\( y \)[/tex] and [tex]\( z \)[/tex] item should be multiplied by [tex]\( 1.59 \)[/tex] individually.
D. [tex]\( (1.09 + 1.59)(x + y + z) \)[/tex]
- This option is incorrect because it adds the costs [tex]\( 1.09 \)[/tex] and [tex]\( 1.59 \)[/tex] together and then multiplies the sum by the total number of items [tex]\( x + y + z \)[/tex], which does not correctly reflect the separate pricing structure.
Therefore, the expression that correctly represents the total amount Max spent at the bakery is:
[tex]\[ \boxed{1.09 x + 1.59 y + 1.59 z} \][/tex]
The correct answer is option [tex]\( \text{B} \)[/tex].
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