Q: A nurse mixes $$x cc of a$$ $$12\%$$ solution and $$y cc of an$$ $$8\%$$ solution to get $$20 cc of a$$ $$9\%$$ solution. Which system of equations represents this scenario?

$$x + y = 20$$ and $$0.12x + 0.08y = 0.09 \times 20$$

Question 1

An investor has $$2900 to $$invest in two accounts. One account yields $$12\%$$ annual interest, and the other yields $$8\%$$ annual interest. If the investor wants to earn a total annual income of $$290$$, how much should be invested in each account?

Accepted Answer

Invest $$\725$ at 8$$\%$$ and $$\$$2175 at$$ $$12\%.$$

Question 2

A nurse needs to mix a $$12\%$$ medication solution with an $$8\%$$ solution to obtain $$20 cc of a$$ $$9\%$$ solution. How many cc of the $$12\%$$ solution should be used?

Accepted Answer

$$5 cc$$

Question 3

Given the equation $$17x + 0.08y = 290$$ and $$x + y = 2900$$, which system of equations best models the investment scenario where $$x is $$the amount invested at $$12\%$$ and $$y at$$ $$8\%$$?

Accepted Answer

$$0.12x + 0.08y = 290$$ and $$x + y = 2900$$

Question 4

A nurse mixes $$x cc of a$$ $$12\%$$ solution and $$y cc of an$$ $$8\%$$ solution to get $$20 cc of a$$ $$9\%$$ solution. Which system of equations represents this scenario?

Accepted Answer

$$x + y = 20$$ and $$0.12x + 0.08y = 0.09 	imes 20$$

Question 5

If $$x cc of$$ $$12\%$$ solution and $$y cc of$$ $$8\%$$ solution are mixed to make $$20 cc of$$ $$9\%$$ solution, what is the value of $$x$$?

Accepted Answer

$$5 cc$$

Question 6

An investor splits $$2900$$ between two accounts, one at $$12\%$$ and one at $$8\%$$ interest. If $$x is $$the amount at $$12\%$$, which equation represents the total interest earned?

Accepted Answer

$$0.12x + 0.08(2900 - x) = 290$$

Question 7

A nurse has $$12\%$$ and $$8\%$$ solutions. To make $$20 cc of$$ $$9\%$$ solution, how much $$8\%$$ solution is needed?

Accepted Answer

$$15 cc$$

Question 8

If $$x cc of$$ $$12\%$$ solution and $$y cc of$$ $$8\%$$ solution are mixed to make $$20 cc of$$ $$9\%$$ solution, what is the value of $$y$$?

Accepted Answer

$$15 cc$$

Question 9

Which of the following is the correct method to solve for the amount invested at $$12\% if $$the total investment is $$2900$$ and the total interest is $$290$$?

Accepted Answer

Set up $$x + y = 2900$$ and $$0.12x + 0.08y = 290$$, then solve the system.

Question 10

A nurse needs to prepare $$20 cc of a$$ $$9\%$$ solution using $$12\%$$ and $$8\%$$ solutions. What is the total amount of pure medication in the final mixture?

Accepted Answer

$$1.8 cc$$

Question 11

An investor wants to earn $$290 in $$interest from $$2900$$ invested in two accounts at $$12\%$$ and $$8\%. $$What is the equation for the total interest earned?

Accepted Answer

$$0.12x + 0.08y = 290$$

Question 12

If $$x is $$the amount invested at $$12\%$$ and $$y at$$ $$8\%$$, and $$x + y = 2900$$, which expression gives the total interest?

Accepted Answer

$$0.12x + 0.08y$$

Question 13

A nurse mixes $$x cc of$$ $$12\%$$ solution and $$y cc of$$ $$8\%$$ solution to get $$20 cc of$$ $$9\%$$ solution. What is the equation for the total amount of medication in the mixture?

Accepted Answer

$$0.12x + 0.08y = 1.8$$

Question 14

An investor splits $$2900$$ between two accounts at $$12\%$$ and $$8\%$$ interest. If $$x is $$the amount at $$12\%$$, what is the amount at $$8\%$$?

Accepted Answer

$$2900 - x$$

Question 15

A nurse mixes $$5 cc of$$ $$12\%$$ solution and $$15 cc of$$ $$8\%$$ solution. What is the concentration of the resulting $$20 cc $$solution?

Accepted Answer

$$9\%$$

Question 16

If an investor puts $$x$$ dollars at $$12\%$$ and the rest at $$8\%$$ for a total of $$2900$$, which equation represents the total investment?

Accepted Answer

$$x + y = 2900$$

Question 17

A nurse needs to mix $$12\%$$ and $$8\%$$ solutions to get $$20 cc of$$ $$9\%$$ solution. What is the equation for the total volume?

Accepted Answer

$$x + y = 20$$

Question 18

An investor wants to earn $$290 in $$interest from $$2900$$ invested at $$12\%$$ and $$8\%. If$$ $$x is $$the amount at $$12\%$$, what is the equation for the interest from the $$8\%$$ account?

Accepted Answer

$$0.08(2900 - x)$$

Question 19

A nurse mixes $$x cc of$$ $$12\%$$ solution and $$y cc of$$ $$8\%$$ solution to get $$20 cc of$$ $$9\%$$ solution. What is the equation for the total amount of solution?

Accepted Answer

$$x + y = 20$$

College Algebra Study Notes: Mixture and Investment Word Problems

Guida di studio - Domande di pratica

Study guide - Flashcard