Question

bill and mary ann went to the viola bakery. bill bought 3 danishes and 8 filled donuts for $14.91. mary ann bought 5 of each for $12.35. what is the price of each type of pastry? the price of a danish is $ 0.97. (simplify your answer.) the price of a filled donut is $\square. (simplify your answer.)

Explanation:

Step1: Define Variables

Let \( d \) be the price of a danish (in dollars) and \( f \) be the price of a filled donut (in dollars).

Step2: Set Up Equations

From Bill's purchase: \( 3d + 8f = 14.91 \)
From Mary Ann's purchase: \( 5d + 5f = 12.35 \)

We know \( d = 0.97 \), substitute into Mary Ann's equation to verify or use Bill's equation to find \( f \). Let's use Bill's equation. Substitute \( d = 0.97 \) into \( 3d + 8f = 14.91 \):

Step3: Substitute and Solve for \( f \)

\( 3(0.97) + 8f = 14.91 \)
\( 2.91 + 8f = 14.91 \)
Subtract 2.91 from both sides: \( 8f = 14.91 - 2.91 = 12 \)
Divide by 8: \( f = \frac{12}{8} = 1.5 \)

Answer:

The price of a filled donut is \(\$1.50\)