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

Step2: Simplify Mary Ann's Equation

Divide the second equation by 5: \( d + f = \frac{12.35}{5}=2.47 \), so \( f = 2.47 - d \)

Step3: Substitute into Bill's Equation

Substitute \( f = 2.47 - d \) into \( 3d + 8f = 14.91 \):
\( 3d + 8(2.47 - d)=14.91 \)
\( 3d + 19.76 - 8d = 14.91 \)
\( - 5d=14.91 - 19.76 \)
\( - 5d=-4.85 \)

Step4: Solve for \( d \)

Divide both sides by - 5: \( d=\frac{-4.85}{-5}=0.97 \)

Answer:

The price of a danish is \(\$0.97\)