UND MATHEMATICS TRACK MEET Team Test 1

University of North Dakota Grades 9/10
January 12, 2026
School Team Name
Calculators are allowed. Key

• 1.

  Determine exactly the value of $x$ for which ${\displaystyle \frac{3x-5}{2}}={\displaystyle \frac{5}{4}}$.

    (20 pts) 1. ${\displaystyle \frac{5}{2}}$

• 2.

  If $a$ and $b$ are positive real numbers and $\frac{a^2+b^2}{\frac{1}{a^2}+\frac{1}{b^2}}=10$, determine exactly the value of $\frac{a^3+b^3}{\frac{1}{a^3}+\frac{1}{b^3}}$.

    (20 pts) 2. $10\sqrt{10}$

• 3.

  $a$, $b$, and $c$ are positive integers such that the sum of $a$ and $b$ is $3$ more than the value of $c$, the value of $a$ is double that of $b$, and the value of $b$ is five less than $c$. Determine exactly the value of $b$.

    (20 pts) 3. 4

• 4.

  The base of a triangular flower bed is $4$ meters longer than its height. If the area of the flower bed is $30$ m², find the height of the triangle.

    (20 pts) 4. $6$ m

• 5.

  Determine exactly the coordinates of the intersection of the lines $x+y=15$ and $5x+8y=87$.

    (20 pts) 5. $(11,4)$

• 6.

  Buddy delivers the same number of local newspapers every day during the summer. He gets paid $\mathrm{\$}0.25$ for each paper delivered, except on Sundays, when he gets paid $\mathrm{\$}1.00$ per paper. After three full weeks, Buddy has earned $\mathrm{\$}900$. how many papers does he deliver daily?

    (20 pts) 6. $120$

• 7.

  Five years ago, Maria was three times as old as Alex. Five years from now, Maria will be twice as old as Alex. What is Alex’s current age?

    (20 pts) 7. $15$

• 8.

  Find the constants $A$, $B$, and $C$ such that ${\displaystyle \frac{A}{(x-2)(x-4)}}+{\displaystyle \frac{B}{x-2}}+{\displaystyle \frac{C}{x(x-4)}}={\displaystyle \frac{1}{x}}$ for all permissible $x$.

    (20 pts) 8. $A=2$, $B=1$, $C=-4$

• 9.

  $(x,y)$ is the intersection of ${\displaystyle \frac{3x}{y}}-4=11$ and $x-y=44$. Determine the value of $x+y$.

    (20 pts) 9. $66$

• 10.

  How many pairs of positive integers $(x,y)$, where $x+y\le 2026$, satisfy the equation ${\displaystyle \frac{x+y^{-1}}{x^{-1}+y}}=11$?

    (20 pts) 10. $168$