Heart of Algebra Word Problems, Functions, and Systems


  1. What is one possible value of f ? 10/3>12f20>7/6
  2. Line q passes through the origin and (s, s+4). It is also perpendicular to line r. If line r follows 1/2x+2/3y=6, find the value of 2s+8.
  3. Line n intersects the y-axis at 5 and is a horizontal line with a slope of zero. Line n intersects 3x5/3y=10 at which point?
  4. A piano duo requires 2 students at two pianos. How many duos could be formed from 12 students?
  5. Line f intersects line e at (4, 12). If line e  follows y=6x12, find the y – intercept for line f if line f also passes through (-8, -1).
  6. Line z intersects the y-axis at a value of -8 and intersects y=34x+9 at an x value of 2. Write the equation of line z in y=ax+b form. Find the value of a+b.
  7. Find a value for a such that the system of equations below has infinite solutions. 4x12y=70 ; ax3y=35/2
  8. Frankie drives 80 miles in 3 hours and another 75 miles in 5 hours. What is the value of his average rate?
  9. 12xy=8x+40x+6y=50 Find the value of yx.
  10. Tam’s Club sells 6c cartons of calculators per box and 12m boxes per day. How many cartons are sold in a year?
  11. Tabitha waters 7 plants per day. If there are 8m plants per garden and 2x gardens per neighborhood, how long would it take her to water 12 neighborhoods?
  12. The line t passes through (6,8) and is perpendicular to 9x12y=90. If line t can be written as ax+by=c, where a, b, and c are constants, find a possible value of a+b.
  13. Line s is parallel to a line with a y-intercept of 6 and x-intercept of -5. If line s passes through (7, 15) find the y-intercept of line s.
  14. 2x7y=80 and yx=10. Find all solutions for x and y.
  15. 3x+11y=-50 and  35x+10=-115y. Find all solutions for x and y.