Jayden has x nickels and y pennies. He has at most 14 coins worth no less than $0.34 combined. Solve this system of inequalities
graphically and determine one possible solution.
1 answer:
Answer:
Step-by-step explanation:
Number of nickels with Jayden = x
Number of pennies with Jayden = y
Since, number of coins is at most 14,
x + y ≤ 14 -------(1)
Worth of nickels = $0.05x
Worth of pennies = $0.01y
Since, worth of pennies is not less than $0.34,
0.05x + 0.01y ≥ 0.34
5x + y ≥ 34 --------(2)
By using a graphing calculator,
Common point of of both the inequalities is (5, 9)
Therefore, Number of nickels = 5
Number of pennies = 9
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They did not include the constraint for y ≤x+3 on the graph.
See attached picture with added constraint.
Using the 4 points that are given as the solution on the graph, replace t he x and Y in the original equation to solve and see which is the greater value.
Point (0,3) P = -0 +3(3) = 0+9 = 9
Point (1,4) P = -1 + 3(4) = -1 +12 = 11
Point (0,0) P = -0 + 3(0) = 0 + 0 = 0
Point (3,0) P = -3 + 3(0) = -3 + 0 = -3
The correct solution to maximize P is (1,4)
Answer:
Step-by-step explanation:
When converting mixed numbers (such as the one above), to improper fractions, we must first multiply the whole number by the denominator:
Then, add the numerator the the product:
Now, put the sum over the denominator to get your solution:
-
To check your work, you can convert the improper fraction to a mixed number to make sure you will end up with .
Divide into
:
with a remainder of
Put the remainder over the denominator:
Therefore, our solution is correct!