Problem A:
Jack has $\$800$ invested in two accounts. One pays $5\%$ interest per year and other pays $10\%$
interest per year. The amount of yearly interest is the same as he would get if the entire $\$800$ was
invested at $8.75\%$. How much does he have invested at each rate?
Problem B:
Jill has $800$ L of acid solution. She obtained it by mixing some $5\%$ acid with some $10\%$ acid. Her final
mixture of $800$ L is $8.75\%$ acid. How much of each of the $5\%$ and $10\%$ solutions did she use to get her final
mixture?
a.) Solve Problem A
b.) Solve Problem B
c.) Explain the similarities between the processes used in solving Problems A and B
In problem (a), let $x$ represent the amount invested at $5\%$ interest, and in problem (b), let $y$ represent
the amount of $5\%$ acid used.
a.) Step 1: Read the problem, we are required to determine the amount invested at each account.
Step 2 : Assign the variable. Then organize the information in the table.
Let $x = $ amount invested at $5\%$ interest.
Then, $800 -x =$ amount invested at $10\%$ interest.
$
\begin{array}{|c|c|c|c|c|c|}
\hline
& \rm{Principal} & \cdot & \text{Interest rate} & = & \rm{Interest} \\
\hline
5 \% & x & \cdot & 0.05 & = & 0.05x \\
\hline
10\% & 800 - x & \cdot & 0.10 & = & 0.10(800 - x) \\
\hline
\end{array}
$
Step 3: Write an equation from the last column of the table
$0.05x + 0.10 (800 -x) = 0.0875(800)$
Step 4: Solve
$
\begin{equation}
\begin{aligned}
0.05x + 80 - 0.10x &= 70\\
\\
-0.05x &= 70 - 80\\
\\
-0.05x &= -10\\
\\
x &= 200
\end{aligned}
\end{equation}
$
Then, by substitution
$800 - x = 800 - 200 = 600$
Step 5: State the answer
In other words, the amount invested at $5\%$ and $10\%$ interest rates is $\$250$ and $\$600$ respectively.
b.) Step 1: Read the problem, we are required to determine quantity of each solutions used.
Step 2 : Assign the variable. Then organize the information in the table.
Let $x = $ amount of $5\%$ acid used.
Then, $800 - y =$ amount of $10\%$ acid used.
$
\begin{array}{|c|c|c|c|c|c|}
\hline
& \text{Liters of solution} & \cdot & \text{Percent Concentration} & = & \rm{Quantity} \\
\hline
5\% & y & \cdot & 0.05 & = & 0.05y \\
\hline
10\% & 800 - y & \cdot & 0.10 & = & 0.10(800 - y) \\
\hline
\end{array}
$
Step 3: Write an equation from the last column of the table
$0.05y + 0.10 (800 - y) = 0.0875(800)$
Step 4: Solve
$
\begin{equation}
\begin{aligned}
0.05y+ 80 - 0.10y &= 70\\
\\
-0.05y &= 70 - 80\\
\\
-0.05y &= -10\\
\\
y &= 200
\end{aligned}
\end{equation}
$
Then, by substitution
$800 - y = 800 - 200 = 600$
Step 5: State the answer
In other words, the final mixture she must use is $200$ L of $5\%$ acid solution and $600$ L
of $10\%$ acid solution.
c.) In general, solving part A and B is similar in a way that the total amount or quantity
is equated with the sum of the individual amounts or quantities of each condition.
Friday, October 11, 2013
Intermediate Algebra, Chapter 2, 2.3, Section 2.3, Problem 68
Subscribe to:
Post Comments (Atom)
Why is the fact that the Americans are helping the Russians important?
In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...
-
There are a plethora of rules that Jonas and the other citizens must follow. Again, page numbers will vary given the edition of the book tha...
-
The only example of simile in "The Lottery"—and a particularly weak one at that—is when Mrs. Hutchinson taps Mrs. Delacroix on the...
-
A good thesis statement presents a claim (an interpretive stance on a story that can be defended using textual evidence) and is a position w...
-
The given two points of the exponential function are (2,24) and (3,144). To determine the exponential function y=ab^x plug-in the given x an...
-
What does the hot air balloon symbolize? To the Assad son who buys the hot air balloon, it symbolizes a kind of whimsy that he can afford. B...
-
The play Duchess of Malfi is named after the character and real life historical tragic figure of Duchess of Malfi who was the regent of the ...
-
Allie’s baseball mitt is extremely important to Holden in The Catcher in the Rye. It is a symbol of Allie since it was important to his brot...
No comments:
Post a Comment