Word Problems

Question 1

Algebraic Translations

Answer 1

• Backsolve or translate into a 2-equation system and solve algebraically?
• Solve systems with substitution (isolate a variable) or by elimination
  (stack the equations and then add or subtract) ?

“of” = multiply
“percent” = 1/100
“verb” = equal sign
“ratio of x to y” = x/y
“total” = sum
“8 less than x” = x - 8

“there are __ as many ..” = __ goes on 2nd thing
(there are 2/3 as many boys as girls —> b = 2/3g)

Question 2

Rates/Work/Distance

Answer 2

Question 3

Statistics

Answer 3

see “avg”? calculate sum
- range: diff between highest & lowest data points
- median: arrange in order. If odd # of things, median is the middle data
point. If even # of things, median is the avg. of middle two data points.

• standard deviation: need distance of each data point from average.
  the farther the data points are from avg, the bigger the standard deviation
• if avg is 40 and standard deviation is 3, then the interval within one
  standard deviation of the mean is 37 to 43.
• weighted averages (the distance the middle number is from each
  endpoint is the ratio, in reverse) 20% of boys and 50% of girls at my
  school drink tea. Overall, 33% of students drink tea.
  (33 is 13 away from 20. 33 is 17 away from 50. So ratio of B:G is 17:13)

Question 4

Evenly Spaced Sets

Answer 4

Median = Average (midpoint of the set)

Adding up evenly spaced sets: Sum = (Avg)*(#)
- Avg = Avg of the 1st and Last term
- # of terms = (Range/Spacing) + 1

Question 5

Overlapping Sets

Answer 5