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

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