Bosco

   At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15.     

   Gary orders a bagel and a muffin, which comes out to $3.50.     

   Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15.     

   How many cents does one bagel cost?     

                                  T + B = 315 ¢     ==>>      T = 315 – B     

                                  B + M = 350 ¢     ==>>     M = 350 – B     

                                   T + 2B + 3M  =  815 ¢     

                                   (315 – B)  +  2B  +  [3 • (350 – B)]  =  815     

                                   315 – B + 2B + 1050 – 3B  =  815     

                                    – 2B + 1365  =  815     

                                    – 2B  =  – 550     

                                         B  =  275 ¢     

   _.     

   I have to paint one side of a wall.  The wall is 12 meters tall and 120 meters long.     

   Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then     

   what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall?     

       12 m / 0.3048 m/ft  =    39.3701 ft     

     120 m / 0.3048 m/ft  =  393.7008 ft     

                          Area  =    39.3701 ft • 393.7008 ft     

                          Area  =    15,500.04 sqft     

                          Paint  =   15,500.04 sqft / 150 sqft/gal     

                          Paint  =   103.33 gal     but you can't buy just 0.33 of a gallon     

                          Paint  =   104 gal     

   _.     

   All members of our painting team paint at the same rate.     

   If 20 members can paint a 2000 square foot wall in 40 minutes, then how long     

   would it take the 20 members to paint a 6000 square foot wall, in minutes?     

   Rate_{20 members}  =  2000 sqft / 40 min  =  50 ^sqft / _min     

     6000 sqft     

   ––––––––––  =  120 min     

     50 ^sqft / _min     

   confirm answer     

   Think of the 6000 sqft wall as being three 2000 sqft walls.     

   Looking at it that way, it would take (3 x 40 min) = 120 min.     

   _.     

   In a store window, there was a box of berries having a total weight of 200 kg.     

   The berries were 99% water, by weight.  After two days in the sun, the water     

   content of the berries was only 90%, by weight.  What was the total weight     

   of the berries after two days, in kg?     

   You're starting with 200 kg of berries, and 99% of that is water.     

   Since they're 99% water, then the other 1% is the solid stuff,     

   and 1% of 200 kg means that there are 2 kg of solid stuff.     

   Some of the water evaporates in the sun, but the solid stuff doesn't.     

   So, after the evaporation, there still remains the same 2 kg of solid stuff.     

   Since the new water content is 90%, that means that now the solid stuff is 10%.     

   So 2 kg (solid stuff) is 10% of the total weight.  (0.10) W = 2   ==>>  W = 2 / 0.10     

   Therefore, the new total weight is 20 kg.     

   _.     

   Find an angle ϴ such that 0°≤ϴ≤360° and ϴ is coterminal with 1500°.     

   1500 / 360  =  4 R 60     ==>>     theta is 60^o     

   _.     

   how do you find the y intercept     

   Substitute zero for x in the equation, then solve it for y.     

   Example:                       y = x – 13     

   set x equal to zero         y = 0 – 13     

                                         y = – 13        <<==  the y-intercept is y = – 13     

   _.     

   The first term of an arithmetic sequence is 2. The sum of the third and the sixth terms is 14. What is the third term?     

   (a₁ + 2d) + (a₁ + 5d)  =  14     

   ( 2 + 2d)  + ( 2 + 5d)  =  14     

                         7d + 4  =  14     

                               7d  =  10     

                                 d  =  10 / 7     

                    2 + 20 / 7  =  34 / 7     

   check answer     

   Does (34 / 7) + (64 / 7)  =  14  ?     

                             98 / 7   =  14  ?     

                                   14  =  14  True     

   _.     

   What is the greatest prime factor of the sum of the arithmetic sequence 1 + 2 + 3?     

   1 + 2 + 3 = 6  The factors of 6 are 1, 2, 3, & 6.  Two prime factors, the greater is 3.     

   _.     

What real value of $t$ produces the smallest value of the quadratic $t^2 -9t - 36 + 13t - 60$?     

                                                                         t² – 9t – 36 + 13t – 60     

collect like terms                                               t² + 4t – 96     

The lowest value will be the vertex, can be     

found by setting the 1st derivitive to zero        2t + 4 = 0   ==>>   t = – 2     

At t = –2, the quadratic equals –100.     

_.     

   All the sides of a triangle are integers.  If the perimeter of the triangle is $3,$     

   then how many different possible triangles are there?     

   Three sides, all integers, total three.  Only one triangle can fit that description.     

   _.     

   The distance from Capital City to Little Village is 5 miles.     

   The distance from Capital City to Mytown is 2 miles.     

   The distance from Mytown to Yourtown is 3 miles.     

   The distance from Little Village to Yourtown is 4 miles.     

   Find the distance from Capital City to Yourtown, in miles.     

   My Town ----- 2 ----- Capital City ----- 1 ----- Your Town ----- 4 ----- Little Village     

   _.     

   find the exact area of the circle with a circumference of 8pi yards.     

   C = π d      ==>>     8 π  =  π d   ==>>     d  = 8     

    r =  d / 2    ==>>     r  =  8 / 2      ==>>     r  = 4     

   A = π r²     ==>>     A = (3.1416) (4²)     

                                      =  3.1416 x 16     

                                      =  50.27 yd³      

   _.