To determine the correct expression that represents the total amount Max spent at the bakery, we need to break down the costs associated with each type of item he buys and then sum these amounts.
1. Price of each item:
- Each glazed donut costs [tex]$1.09.
- Each cinnamon bagel costs $[/tex]1.59.
- Each onion bagel costs $1.59.
2. Variables:
- Let [tex]\( x \)[/tex] represent the number of glazed donuts Max buys.
- Let [tex]\( y \)[/tex] represent the number of cinnamon bagels Max buys.
- Let [tex]\( z \)[/tex] represent the number of onion bagels Max buys.
3. Calculation of total cost:
- Cost of [tex]\( x \)[/tex] glazed donuts: [tex]\( 1.09 \times x \)[/tex]
- Cost of [tex]\( y \)[/tex] cinnamon bagels: [tex]\( 1.59 \times y \)[/tex]
- Cost of [tex]\( z \)[/tex] onion bagels: [tex]\( 1.59 \times z \)[/tex]
4. Total amount spent by Max:
- To find the total amount, we add the costs of all items:
[tex]\[
1.09x + 1.59y + 1.59z
\][/tex]
Let's examine the options:
A. [tex]\( 1.09x + 1.59yz \)[/tex]
- This expression is incorrect because it implies multiplying [tex]\( y \)[/tex] and [tex]\( z \)[/tex] together, which is not how the total cost is computed.
B. [tex]\( 1.09x + 1.59y + 1.59z \)[/tex]
- This expression is correct because it adds the costs of all items individually and matches the derived total amount.
C. [tex]\( 1.09x + 3.18(y + z) \)[/tex]
- This expression is incorrect because it incorrectly multiplies the sum [tex]\( y + z \)[/tex] by [tex]\( 3.18 \)[/tex]. Even though [tex]\( 3.18 = 1.59 \times 2 \)[/tex], it does not distribute properly according to the actual cost structure.
D. [tex]\( (1.09 + 1.59)(x + y + z) \)[/tex]
- This expression is incorrect because it adds the prices of the glazed donuts to the bagels' price and then multiplies the sum of the quantities, which does not represent the actual totals.
Therefore, the correct answer is option B:
[tex]\[
1.09 x + 1.59 y + 1.59 z
\][/tex]
