Algebra Word Problem Solutions

If you have a loan for $5000 with .03% interest to be paid off in 24 months and you have 15 months left, then how much do you owe?

To print his first novel, Shane can use a print-on-demand book printer or he can buy a printer. The book printer charges a setup fee of $150 plus $6 per copy of the book. The printer he would need costs $750, and it would cost $2 per copy to print the book. For how many copies are the costs the same?

Mr. Krogman usually prices the umbrellas in his store at $8 each. However, on rainy days he increases the price by 75%. How much does he charge for an umbrella on a rainy day?
A $2
B $6
C $9.38
D $14

What is the complete factorization of ${\displaystyle 6x^4+12x^2}$?

3y - 8y = 25

A yoga studio charges a $36 membership fee and a $20.60 per month for 10 classes. A Martial Arts studio charges a $20 membership fee and $22.20 per month for 10 classes. Your friend belongs to the yoga studio the same month you belong to the Martial Arts studio. After how many months is your friend's total cost the same as your total cost?

The parallel lines at the right are cut by a transversal. Find the value of x.
a. Angles 1 and 2 are corresponding angles, ${\displaystyle m\angle 1=45°}$, and ${\displaystyle m\angle 2=(x+25)°}$.
b. Angles 3 and 4 are alternate interior angles, ${\displaystyle m\angle 3=2x°}$, and ${\displaystyle m\angle 4=80°}$.

4s=24

Prove: If x and y are real numbers with x<y, then there are infinitely many rational numbers in the interval [x,y]

−3x+11=2

Find the eighth term of the arithmetic sequence whose first term is 4 and whose common difference is -7.

Solve for x. ${\displaystyle \log 7(x+6)=0}$

${\displaystyle x^2+2x-1=x^2-x+2}$

45% of s is 18

Sarah's craft project uses pieces of yarn that are $\frac{1}{8}$ yard long. She has a piece of yarn that is 3 yards long. How many $\frac{1}{8}$-yard pieces can she cut and still have 1 $\frac{1}{4}$ yards left?

A computer repair technician charges $50 per visit plus $30/h for house calls.
a) Write an algebraic expression that describes the service charge for one household visit.
b) Use your expression to find the total service charge for a 2.5-h repair job.

Solve linear equation and check: $7x+3=6(x-1)+9$

An objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints.
b. Find the value of the objective function at each corner of the graphed region.
c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.
${\displaystyle z=2x+3y}$
${\displaystyle \{\begin{array}{c}x\text{and}y\ge 0\\ 2x+y\le 8\\ 2x+3y\le 12\end{array}}$

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like a stirred tank. Suppose the blood volume is a four-liter tank that initially has a zero concentration of a particular drug. At time ${\displaystyle t=0}$, an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500 mg/L. The inflow rate is 0.06 L/min. Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant. a. Write an initial value problem that models the mass of the drug in the blood, for ${\displaystyle t\ge 0}$. Solve the initial value problem, and graph both the mass of the drug and the concentration of the drug. c. What is the steady-state mass of the drug in the blood? d. After how many minutes does the drug mass reach 90% of its steady-state level?

The number multiplied on both sides of the equation ${\displaystyle 0.9x-4.3=0.47}$ in order to clear of decimals.