The research department of a company that manufactures children's fruit drinks is experimenting with a news flavor. A $17.5 \%$ fructose solution is needed, but only $10 \%$ and $20 \%$ solutions are available. How many gallons of the $10 \%$ fructose solution should be mixed with the $20 \%$ fructose solution to obtain 20 gallons of a $17.5 \%$ fructose solution?

If the third term of an arithmetic sequence is 13 and the seventeenth term is - 29, what is the eighth term?

Solve.

The number of cranes born each year in a new aviary forms a sequence whose general term is $a_n=n^2+2 n-1$. Find the number of cranes born in the fourth year and the total number of cranes born in the first four years.

Solve. See the mentioned example.

Mrs. Laser agrees to give her son Mark an allowance of $\$ 0.10$ on the first day of his $14$-day vacation, $\$ 0.20$ on the second day, $\$ 0.40$ on the third day, and so on. Write an equation of a sequence whose terms correspond to Mark's allowance. Find the allowance Mark will receive on the last day of his vacation.

A company that manufactures boxes recently purchased $\$ 2000$ worth of new equipment to offer gift boxes to its customers. The cost of producing a package of gift boxes is $\$ 1.50$ and it is sold for $\$ 4.00$. Find the number of packages that must be sold for the company to break even.

A surveyor stands 150 feet from the base of a viaduct and measures the angle of elevation to be 46.2$^\circ$. His eye level Is 6 feet above the ground. What is the height of the viaduct to the nearest foot?

If the cost, $C(x)$, for manufacturing $x$ units of a certain product is given by $C(x)=x^2-15 x+50$, find the number of units manufactured at a cost of $\$ 9500$.

Solve.

If the cost, $C$, for manufacturing $x$ units of a certain product is given by $C=x^2-15 x+50$, find the number of units manufactured at a cost of $\$ 9500$.

If a certain number is subtracted from the numerator and added to the denominator of $\frac{9}{19}$, the new fraction is equivalent to $\frac{1}{3}$. Find the number.

Hooke's Law $\quad$ Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring.

A force of $220$ newtons stretches a spring $0.12$ meter. What force is required to stretch the spring $0.16$ meter?

According to Boyle's law, the pressure exerted by a gas is inversely proportional to the volume, as long as the temperature stays the same. If a gas exerts a pressure of $1250$ pounds per square inch when the volume is $2$ cubic feet, find the volume when the pressure is $800$ pounds per square inch.

The top three corn producers in the world-the United States, China, and Brazilgrew a total of about 652 million metric tons $\mathrm{(MT)}$ of corn in 2014. The United States produced $70$ million $\mathrm{(MT)}$ more than the combined production of China and Brazil. China produced $141$ million MT more than Brazil. Find the number of metric tons of corn produced by each country.

The cost $C$ of producing $x$ number of scientific calculators is given by $C=4.50 x+3000$, and the revenue $R$ from selling them is given by $R=16.50 x$. Find the number of calculators that must be sold to break even. (Recall that to break even, revenue $=$ cost.)

In the United States, the annual consumption of cigarettes is declining. The consumption $c$ in billions of cigarettes per year since the year $2000$ can be approximated by the formula $c=-9.4 t+431$ where $t$ is the number of years after $2000$. Use this formula to predict the years that the consumption of cigarettes will be less than $200$ billion per year.