MATH $1121$ Worksheet #$5$ Section $1\mathrm{.}5$

Make sure you write and solve a system of equations for each problem!!!

$1.$ A woman has $$500,000$ invested in two rental properties. One yields an annual return of

$10\%$ on her investment, and the other returns $12\%$ on her investment. Her total annual

return from the two investments is $$53,000.$ Let x represent the amount of the $10\%$

investment and let y represent the amount of the $12\%$ investment. Find how much is

invested in each property.

$2.$ A bank lent $$237,000$ to a company for the development of two products. If the loan for

product A was $$69,000$ more than that for product B$,$ how much was lent for each

product?

$3.$ A glass of skim milk supplies $0\mathrm{.}1$ mg of iron and $8\mathrm{.}5$ g of protein. A quarter pound of

lean red meat provides $3\mathrm{.}4$ mg of iron and $22$g of protein. If a person on a special diet is

to have $7\mathrm{.}15$ mg of iron and $73\mathrm{.}75$ g of protein, how many glasses of skim milk and how

many quarter$-$pound servings of meat would provide this?

$4.$ A nurse has two solutions that contain different concentrations of a certain medication.

One is a $20\%$ concentration and the other is a $5\%$ concentration. How many cubic

centimeters of each should he mix to obtain $10$ cc of a $15\mathrm{.}5\%$ solution?

$5.$ A concert promoter is selling $16,000$ tickets. If the promoter charges $$40$ for some

tickets and $$60$ for others, how many of each type must be sold to make $$760,000?$

$6.$ A social agency is charged with providing services to three types of clients: A$,$ B$,$ and C$.$

A total of $500$ clients are to be served, with $$150,000$ available for counseling and

$$100,000$ available for emergency food and shelter. Type A clients require an average of

$$200$ for counseling and $$300$ for emergencies, type B clients require an average of $$500$

for counseling and $$200$ for emergencies, and type C clients require an average of $$300$

for counseling and $$100$ for emergencies. How many of each type of client can be

served? $($Hint: This problem will require you to set up a system of $3$ equations with $3$

unknowns. To solve this, first use the elimination method to eliminate one of the

variables and turn the problem into a system with $2$ equations and $2$ unknowns.$)$