Question 322729: Audrey has 32 dimes and quarters in her piggy bank with a total value of $6.50. How
many of the coins are dimes and how many are quarters?
A) 15 dimes and 20 quarters
B) 10 dimes and 22 quarters
C) 20 dimes and 18 quarters
D) 22 dimes and 10 quarters
When applying the Test Point method to a graphed linear inequality, what is the best
option to pursue if the test point you choose fails to satisfy the linear inequality?
A) Report the error to your instructor so that he or she is aware that the inequality has
no solution.
B) Continue to choose test points until you find one that satisfies the inequality.
C) Shade the opposite half-plane.
D) Shade the half-plane containing the point.
Determine which of the ordered pairs (3, 2), (–3, 4), (–1, –5), and (1, –6) satisfy the
compound inequality.
y < –2x and y > x
Write as a single interval if possible: [–15, ∞)∪(–7, ∞)
A) (–15, ∞)
B) [–15, ∞)
C) (–7, ∞)
D) [–15, ∞)∪(–7, ∞)
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! Problem 1:
To solve this problem you are going to write two equations using the given information.
First,you know that Audrey has 32 dimes and quarters:
D + Q = 32 (D= number of dimes, Q= number of quarters)
You can also rewrite this as D = 32-Q
Second, you know that the total value of these coins is $6.50 and the value of a dime is $0.10 and a quarter is $0.25:
0.10(D) + 0.25(Q) = 6.50
Now plug in the first equation into the second equation and solve for Q:
0.10(D) + 0.25(Q) = 6.50
0.10*(32-Q) + 0.25(Q) = 6.50
3.2 - 0.1Q + 0.25Q = 6.50
3.2 + 0.15Q = 6.50
0.15Q = 3.30
Q = 22
So there are 22 quarters.
Now plug that value into the first equation to find the number of dimes:
D + Q = 32
D + 22 = 32
D = 10
So the answer is B, 10 dimes and 22 quarters.
Problem 2:
You want to shade the half that makes the inequality true. So since the test point was wrong, you should shade the other half-plane, or answer C.
Problem 3:
Looking at the second equation, you know that y>x. Looking at the listed ordered pairs, only one satisfies this criteria, and that is (-3,4). Plug these x and y values in to verify that this is the correct answer.
Problem 4:
The answer is B because a union includes all points, even if they are only listed in one of the intervals.
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