Q: If $x$ liters of a $20\%$ alcohol solution are mixed with $12$ liters of a $12\%$ solution to obtain a $14\%$ solution, which equation represents the total amount of alcohol in the mixture?

$0.20x + 0.12 \times 12 = 0.14(x + 12)$

Q: If you mix $x$ liters of $10\%$ alcohol solution with $40$ liters of $50\%$ solution to obtain a $40\%$ solution, which equation represents the total alcohol content?

$0.10x + 0.50 \times 40 = 0.40(x + 40)$

Question 1

The Vietnam Veterans Memorial in Washington, DC, is shaped like two sides of an isosceles triangle. If the two walls of equal length are joined by a straight line of $438$ ft, and the perimeter of the resulting triangle is $931.5$ ft, what is the length of each wall?

Accepted Answer

$496.75$ ft

Question 2

David sold his house for $159,000. He knew he would have to pay a $6\%$ commission to his agent. What amount did he have after the agent was paid?

Accepted Answer

$149,460$

Question 3

Michele invested some money at $4.5\%$ simple interest and $1000$ less than twice this amount at $3\%$. Her total annual income from the interest was $1020$. How much did she invest at each rate?

Accepted Answer

$4000$ at $4.5\%$, $7000$ at $3\%$

Question 4

Piotr invested some money at $3.5\%$ simple interest, and $5000$ more than three times this amount at $4\%$. He earned $1440$ in annual interest. How much did he invest at each rate?

Accepted Answer

$4000$ at $3.5\%$, $17,000$ at $4\%$

Question 5

In a chemistry class, $12$ L of a $12\%$ alcohol solution must be mixed with a $20\%$ solution to obtain a $14\%$ solution. How many liters of the $20\%$ solution are needed?

Accepted Answer

$6.0$ L

Question 6

How many liters of a $10\%$ alcohol solution must be mixed with $40$ L of a $50\%$ solution to obtain a $40\%$ solution?

Accepted Answer

$13.33$ L

Question 7

A triangle has sides of length $x$, $x$, and $438$ ft, and its perimeter is $931.5$ ft. Which equation can be used to solve for $x$?

Accepted Answer

$x + x + 438 = 931.5$

Question 8

If $x$ liters of a $20\%$ alcohol solution are mixed with $12$ liters of a $12\%$ solution to obtain a $14\%$ solution, which equation represents the total amount of alcohol in the mixture?

Accepted Answer

$0.20x + 0.12 	imes 12 = 0.14(x + 12)$

Question 9

A real estate agent earns a $6\%$ commission on the sale price of a house. If the agent received $A$ dollars in commission for a house sold at price $P$, which equation represents this relationship?

Accepted Answer

$A = 0.06P$

Question 10

Michele invested $x$ dollars at $4.5\%$ and $(2x - 1000)$ dollars at $3\%$. Her total annual interest is $1020$. Which equation models this situation?

Accepted Answer

$0.045x + 0.03(2x - 1000) = 1020$

Question 11

Piotr invested $x$ dollars at $3.5\%$ and $(3x + 5000)$ dollars at $4\%$. His total annual interest is $1440$. Which equation models this situation?

Accepted Answer

$0.035x + 0.04(3x + 5000) = 1440$

Question 12

A solution contains $40$ L of $50\%$ alcohol. How much $10\%$ alcohol solution should be added to obtain a $40\%$ alcohol solution?

Accepted Answer

$13.33$ L

Question 13

If you mix $x$ liters of $10\%$ alcohol solution with $40$ liters of $50\%$ solution to obtain a $40\%$ solution, which equation represents the total alcohol content?

Accepted Answer

$0.10x + 0.50 	imes 40 = 0.40(x + 40)$

Question 14

A triangle has two equal sides and a base of $438$ ft. If the perimeter is $931.5$ ft, what is the formula to find the length of the equal sides?

Accepted Answer

$x = \frac{931.5 - 438}{2}$

Question 15

A chemistry student needs to mix $12$ L of $12\%$ alcohol solution with $x$ L of $20\%$ solution to obtain a $14\%$ solution. What is the value of $x$?

Accepted Answer

$6$ L

Question 16

If a house is sold for $P$ dollars and the agent's commission rate is $r$, what is the formula for the amount the seller receives after commission?

Accepted Answer

$P - rP$

Question 17

A student invests $x$ dollars at $4.5\%$ and $(2x - 1000)$ dollars at $3\%$. If the total interest is $1020$, what is the value of $x$?

Accepted Answer

$4000$

Question 18

Piotr invests $x$ dollars at $3.5\%$ and $(3x + 5000)$ dollars at $4\%$ to earn $1440$ in interest. What is the value of $x$?

Accepted Answer

$4000$

Question 19

A chemistry student mixes $x$ liters of $20\%$ alcohol solution with $12$ liters of $12\%$ solution to obtain a $14\%$ solution. What is the value of $x$?

Accepted Answer

$6$ L

College Algebra Applications: Geometry, Percentages, Simple Interest, and Mixture Problems

Study Guide - Practice Questions

Study Guide - Flashcards