Algebra - Developing and Solving Problems
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Harry has $2.25 in Nickels, Dimes and quarters. If he had twice as many nicels, half as many dimes ....
The sume of the digits of a three digit number is 11. If the digits are reversed ...
Find the Vertex, Focus and ...
Find the equation of the parabola ....
Write each equation in the form ...
Find the Vertex, Focus, directrix and axis ...
Graph both equations of each system ...
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Solution Summary
The expert examines developing and solving problems using the quadratic equation. The vertex and focus are determined. A complete, neat and step-by-step solutions are provided in the attached file.
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(1) Let Harry have x nickels, y dimes and z quarters
x + y + z = 27 --- (1)
5x + 10y + 25z = 225, that is x + 2y + 5z = 45 --- (2)
5(2x) + 10(y/2) + 25z = 250, that is 2x + y + 5z = 50 --- (3)
(2) - (1) y + 4z = 18 y = 18 - 4z
(3) - 2 * (2) -3y - 5z = -40
-3(18 - 4z) - 5z = -40
7z = 14
z = 2
y = 18 - 4(2) = 10
x = 27 - y - z = 27 - 10 - 2 = 15
Harry has 15 nickels, 10 dimes and 2 quarters
(2) Let the old number be "abc". Its value is 100a + 10b + c
a + b + c = 11 --- (1)
The new number is "cba". Its value is ...
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