Answered

A bakery sells glazed donuts for $\$ 1.09$ each. Cinnamon bagels and onion bagels are $\$ 1.59$ each. Max buys $x$ donuts, $y$ cinnamon bagels, and $z$ onion bagels. Which expression represents the total amount Max spent at the bakery?


A$1.09 x+1.59 y z$
B$1.09 x+1.59 y+1.59 z$
C$1.09 x+3.18(y+z)$
D$(1.09+1.59)(x+y+z)$

Verified Answer :

  • Define the cost of each item type: glazed donuts (\(1.09x\)), cinnamon bagels (\(1.59y\)), and onion bagels (\(1.59z\)).
  • Add the individual costs together to obtain the total expression: \(1.09x + 1.59y + 1.59z\).
  • Match the resulting expression with the given options to identify the correct choice.
  • The correct option is: \(\boxed{1.09x + 1.59y + 1.59z}\).

Explanation

  1. Analyzing the Total Cost Expression

To find the total amount Max spent at the bakery, we need to calculate the cost of each item purchased and then sum those values. The items are glazed donuts, cinnamon bagels, and onion bagels.

  • The cost of glazed donuts is given by multiplying the unit price, \(\$1.09\), by the quantity of donuts purchased, \(x\). This gives us \(1.09 \times x = 1.09x\).
  • The cost of cinnamon bagels is given by multiplying the unit price, \(\$1.59\), by the quantity of cinnamon bagels purchased, \(y\). This gives us \(1.59 \times y = 1.59y\).
  • The cost of onion bagels is given by multiplying the unit price, \(\$1.59\), by the quantity of onion bagels purchased, \(z\). This gives us \(1.59 \times z = 1.59z\).

The total amount spent is the sum of these three costs: \(1.09x + 1.59y + 1.59z\).

  1. Selecting the Correct Expression

Now that we have the expression for the total cost, we compare it with the given options to select the correct one:

  • Option 1: \(1.09x + 1.59yz\) is incorrect because it treats the product of the number of bagels as a term.
  • Option 2: \(1.09x + 1.59y + 1.59z\) matches our derived expression exactly.
  • Option 3: \(1.09x + 3.18(y + z)\) expands to \(1.09x + 3.18y + 3.18z\), which is incorrect because the unit price for bagels is \(\$1.59\), not \(\$3.18\).
  • Option 4: \((1.09 + 1.59)(x + y + z)\) is incorrect as it implies that every item is sold at a bundled rate, ignoring the specific prices assigned to each item type.

Thus, the correct expression representing the total amount spent is \(1.09x + 1.59y + 1.59z\).

Examples

In everyday shopping, calculating the total cost of a basket of goods requires identifying the price and quantity of each unique item. For instance, if you purchase apples, bananas, and oranges at different unit prices, you calculate the total by finding the subtotal for each fruit (\(price \times quantity\)) and summing them up. This mathematical approach helps in budgeting, verifying receipts, and making informed financial decisions at the grocery store or any other retail establishment. If you buy \(a\) items at price \(p_1\), \(b\) items at \(p_2\), and \(c\) items at \(p_3\), your total cost is always \(\$p_1 \times a + p_2 \times b + p_3 \times c\).

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