Amira... said:
2) Three times the reciprocal of a number plus 7 times the reciprocal of one less than that number is zero. Find original number
i) Pick a variable for "a number".
ii) Write an expression for "the reciprocal of" the number.
iii) Write an expression for "three time" this reciprocal.
iv) Returning to the variable in (i), write an expression for "one less than" the number.
v) Write an expression for "the reciprocal of" the difference created in (iv).
vi) Write an expression for "seven times" the reciprocal in (v).
vii) Sum (iv) and (vi).
viii) Set equal to zero.
ix) Solve for the variable in (i).
Amira... said:
3) David has 87 cents worth of stamps. If he has twice as many 3 cent stamps as 1 cent stamps and 3 more 4 cent stamps than 3 cent stamps, how many of each kind of stamp does he have?
i) Since the three-cent stamps are defined in terms of the one-cent stamps, pick a variable for the number of one-cent stamps.
ii) Write an expression in terms of (i) for the number of three-cent stamps.
iii) Write an expression in terms of (ii) for the number of four-cent stamps.
iv) Write expressions for the values of the stamps. For instance, since three-cent stamps are worth three cents, the value of four of them would be (3)(4). Use your variable instead of "4".
v) Sum the value expressions. Simplify.
vi) Set equal to the given total value.
vii) Solve for the variable.
viii) Back-solve for the numbers of each sort of stamp, using the expressions in (ii) and (iii).
Amira... said:
4) The width of a rectangle is 9 inches shorter than it diagnal and 7 inches shorter than its length. Find the length of the diagnol.
i) Pick a variable for the length.
ii) Write an expression for the width in terms of (i).
iii) Use the Pythagorean Theorem to find an expression, in terms of (i) and (ii), for the diagonal.
iv) Returning to the variable in (i) for the length, and noting that the width is seven less than the length and nine less than the diagonal, compare the diagonal to the length, and create an expression for the diagonal in terms of the variable in (i).
v) Set (iii) equal to (iv).
vi) Solve for the length.
vii) Back-solve, using (iii) or (iv), for the diagonal.
Amira... said:
5) A plane flies at a speed of 800 miles per hour is in still air. it takes 15 minutes longer to fly 1260 miles into the wind than it takes it to fly 1320 miles with the wind. Find speed of wind.
i) Pick a variable for the wind-speed.
ii) Note that the speed against the wind is the engine-speed less the wind-speed, and create an expression, in terms of (i), for the against-the-wind rate.
iii) Note that the speed with the wind is the sum of the speeds. Create an expression, in terms of (i), for the with-the-wind rate.
iv) Note that, given "d = rt", you can solve for "t = d/r". Use this to create two different "time" expressions, one for each direction.
v) Translate "(against-the-wind time) equalled (with-the-wind time) plus (a quarter hour)" into an equation, and solve.
If you get stuck, please reply showing how far you have gotten. Thank you.
Eliz.
