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

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