1. Bill and Mary Ann went to the Viola bakery. Bill bought 4 danishes and 9 filled donuts for $14.20. Mary Ann bought 6 of each for $12.85. What is the price of each type of pastry... 1. Bill and Mary Ann went to the Viola bakery. Bill bought 4 danishes and 9 filled donuts for $14.20. Mary Ann bought 6 of each for $12.85. What is the price of each type of pastry? The price of a danish is $ (Simplify your answer.) The price of a filled donut is $ (Simplify your answer.) 2. How many solutions does the system of equations have? y=-5/2x+4 5x + 2y = 11 A. 1 solution B. no solution C. infinitely many solutions D. cannot be determined 3. Solve the system of equations by using the substitution method. 2x-5y=18 y=x-4 4. A high school football team scores a total of 34 points by scoring touchdowns and field goals. Suppose each field goal is worth 3 points and each touchdown is worth 7 points. Complete parts a and b. a. Let x represent the number of field goals and y represent the number of touchdowns. Write an equation that models the total points scored in the game. Choose the correct answer. 5. Kendall bought 6 notebooks and 3 pens for a total of $35. The cost of one notebook is $1.75 more than the cost of one pen. What is the combined cost of one notebook and one pen?
Understand the Problem
The questions are asking to solve various mathematical problems involving systems of equations, price calculations, and formulating equations based on given scenarios. The high-level approach will involve setting up the equations based on the descriptions provided and solving for the unknowns.
Answer
The price of a danish is $1.01 and the price of a filled donut is $1.13.
Answer for screen readers
The price of a danish is $1.01 and the price of a filled donut is $1.13.
Steps to Solve
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Define the variables for pastries Let the price of a danish be $d$ and the price of a filled donut be $f$.
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Set up the equations based on purchases From Bill's purchase: $$ 4d + 9f = 14.20 $$
From Mary Ann's purchase: $$ 6d + 6f = 12.85 $$
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Simplify the second equation Divide the second equation by 6 to simplify: $$ d + f = 2.14 \quad (1)$$
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Rearrange the equations Rearranging equation (1) gives: $$ f = 2.14 - d \quad (2) $$
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Substitute equation (2) into the first equation Substituting ( f ) in the first equation: $$ 4d + 9(2.14 - d) = 14.20 $$
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Solve for ( d ) Distributing and combining like terms: $$ 4d + 19.26 - 9d = 14.20 $$
Combine terms: $$ -5d + 19.26 = 14.20 $$ $$ -5d = 14.20 - 19.26 $$ $$ -5d = -5.06 $$ $$ d = 1.012 $$
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Find ( f ) using equation (2) Substituting ( d ) back into equation (2): $$ f = 2.14 - 1.012 $$ $$ f = 1.128 $$
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State the final answer Thus, the price of a danish is $1.012 and the price of a filled donut is $1.128.
The price of a danish is $1.01 and the price of a filled donut is $1.13.
More Information
The prices provided are rounded to two decimal places for currency representation. These prices can help understand the relationship between the costs of different baked goods in a similar real-life scenario.
Tips
- Forgetting to distribute correctly when substituting in the equations.
- Not combining like terms properly, which can lead to incorrect values for ( d ) and ( f ).
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