11.8: Proficiency Exam
Proficiency Exam
Solve using graphing:
\(\left\{\begin{array}{r}
3x + 2y = 4\\
15x + 10y = -10
\end{array}\right.\)
- Answer
-
inconsistent
Solve using graphing:
\(\left\{\begin{array}{r}
2x - 3y = 2\\
x + 2y = 8
\end{array}\right.\)
- Answer
-
(4,2)
Solve using substitution:
\(\left\{\begin{array}{r}
2x + 6y = 16\\
x - 4y = -13
\end{array}\right.\)
- Answer
-
\((−1,3)\)
Solve using addition:
\(\left\{\begin{array}{r}
3x + 8y = -5\\
x - 2y = 3
\end{array}\right.\)
- Answer
-
\((1, -1)\)
Solve using either substitution or addition:
\(\left\{\begin{array}{r}
4x - 4y = 8\\
x - y = 5
\end{array}\right.\)
- Answer
-
inconsistent
Solve using either substitution or addition:
\(\left\{\begin{array}{r}
9x + 3y = 12\\
3x - y = 4
\end{array}\right.\)
- Answer
-
\((\dfrac{4}{3}, 0)\)
The sum of two numbers is 43 and the difference of the same two numbers is 7. What are the numbers?
- Answer
-
18 and 25
A chemist needs 80 ml of an 18% acid solution. She has two acid solutions, A and B, to mix together to form the 80-ml solution. Acid solution A is 15% acid and acid solution B is 20% acid. How much of each solution should be used?
- Answer
-
32 ml of solution A; 48 ml of solution B.
A parking meter contains 32 coins. If the meter contains only nickels and quarters, and the total value of the coins is $4.60, how many of each type of coin are there?
- Answer
-
17 nickels and 15 quarters
A person has $15,000 to invest. If he invests part at 8% and the rest at 12%, how much should he invest at each rate to produce the same return as if he had invested it all at 9%?
- Answer
-
$11,250 at 8%; $3,750 at 12%