Let us take number of $5 bills = x and
number of $10 bills = y.
Give that "number of $10 bills is twice the number of $5 bills".
So, y is twice of x,
We can setup an equation.
y= 2x ............................... equation(1)
Total value of all bills = $125.
We can setup another equation,
5*(number of $5 bills) + 10*(number of $10 bills) =125.
5(x) +10(y) = 125 ................................... equation(2)
Plugging y=2x in equation(2), we get
5(x) +10(2x) = 125 .
5x+20x = 125.
Adding like terms
25x = 125
Dividing both sides by 25.
25x /25 = 125/25
x= 5.
Plugging x=5 in first equation, we get
y= 2(5) = 10.
Therefore, number of number of $5 bills=5 bills and number of $10 bills = 10 bills.
Pair 1: slope = (9 - 5)/(8+4) = 1/3
midpoint = ((-4+8)/2, (5+9)/2) = (2, 7)
perpendicular bisector passes through point (2, 7) with slope = -1/(1/3) = -3 giving the equation (y - 7)/(x - 2) = -3 or y - 7 = -3(x - 2) or y = -3x + 13 and y-intercept at y = 13.
Pair 2: slope = (6 - 4)/(-8-2) = -1/5
midpoint = ((2-8)/2, (4+6)/2) = (-3, 5)
perpendicular
bisector passes through point (-3, 5) with slope = -1/(-1/5) = 5 giving
the equation (y - 5)/(x + 3) = 5 or y - 5 = 5(x + 3) or y = 5x + 20
and y-intercept at y = 20.
Pair 3: slope = (2 - 4)/(7 - 5) = -1
midpoint = ((5+7)/2, (4+2)/2) = (6, 3)
perpendicular
bisector passes through point (6, 3) with slope = -1/(-1) = 1 giving
the equation (y - 3)/(x - 6) = 1 or y - 3 = (x - 6) or y = x - 3
and y-intercept at y = -3.
Pair 4: slope = (3 - 9)/(-4 - 2) = 1
midpoint = ((2-4)/2, (9+3)/2) = (-1, 6)
perpendicular
bisector passes through point (-1, 6) with slope = -1(1) = -1 giving
the equation (y - 6)/(x + 1) = -1 or y - 6 = -1(x + 1) or y = -x + 5
and y-intercept at y = 5.
Pair 5: slope = (-12 + 2)/(9 - 3) = -5/3
midpoint = ((3+9)/2, (-2-12)/2) = (6, -7)
perpendicular
bisector passes through point (6, -7) with slope = -1(-5/3) = 3/5 giving
the equation (y + 7)/(x - 6) = 3/5 or 5(y + 7) = 3(x - 6) or 5y = 3x - 53
and y-intercept at y = -10.6.
Pair 6: slope = (12 - 10)/(8 - 4) = 1/2
midpoint = ((4+8)/2, (10+12)/2) = (6, 11)
perpendicular
bisector passes through point (6, 11) with slope = -1(1/2) = -2 giving
the equation (y - 11)/(x - 6) = -2 or y - 11 = -2(x - 6) or y = -2x + 23
and y-intercept at y = 23.
Arrangement in order of y-intercepts from smallest to largest
a(3, -2) and b(9, -12)
a(5, 4) and b(7, 2)
a(2, 9) and b(-4, 3)
a(-4, 5) and b(8, 9)
a(2, 4) and b(-8, 6)
a(4, 10) and b(8, 12)
Answer: The approximate total weight of the grapefruits, using the clustering estimation technique is B. 35 ounces.
We have to calculate speed for 1 lap for all of 'em.
Cutwright - 84/35 = 2.4 mins for 1 lap
Evans- 96.6/42 = 2.3 mins for 1 lap
Liza- 102.6/38 = 2.7 mins for 1 lap
So, EVANS drove fastest among them as he took less time...
