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 ¢     

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A cylindrical container with an 8 in. diameter and an 2 in. height is completely filled with water. All of its contents are poured into another cylindrical container that is 32 in. tall.If the water completely fills the second container, the second container’s diameter is ___ in.     

                                V_cylinder  =  π r² h     

                                V₁  =  (π)(4²)(2) inch³            8 is the diameter so 4 is the radius     

                                V₂  =  (π)(r²)(32) inch³     

                                V₁  =  V₂     

                                (π)(16)(2)  =  (π)(r²)(32)     

cancel out π                 (16)(2)  =  (r²)(32)     

                                            32  =  32r²     

                                              r²  =  1     

                                                r  =  1    

                                               d  =  2r  =  (2)(1)     

                                               d  =  2     

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Consider the following pair of equations: y = −2x + 8 y = x − 1 Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.     

     y  =  – 2x + 8       (equation 1)     

     y =  x – 1             (equation 2)     

     Since (eq 2) informs us that y = x – 1,     

     I will substitute that for the y in (eq 1).     

     x – 1  =  – 2x + 8     

     Gather the like terms.  By convention, locate     

     variables on the left and constants on the right.     

     x + 2x  =  8 + 1     

           3x  =  9     

             x  =  3     

     Substitute 3 for the x in one of the original equations.     

             y  =  3 – 1     

             y  =  2     

     I'll let you write the solution in (x, y) form.     

_.     

The mean of six numbers is 14. If one of the six numbers is removed, the mean becomes 5. What is the value of the number removed?     

5 5 5 5 5 59 will work.     

Here's how I got it:     

6 • 14 = 84     

( 84 – 25 ) = 59     

Other numbers can be used for the first 5,     

just so long as they add up to 25.     

_.     

Find the height of the triangle pictured above, if the area is 40.5     

     A  =  (1 / 2) • base • height     

     40.5  =  (1 / 2) • 9 • h     

     81.0  =  9 • h     

     h  =  81.0 / 9     

     h  =  9.00     rounded to the tenth     h = 9.0     

_.     

Find the average speed for each climb.     
Which average speed is greater?     

a)  24 meters / 10.75 sec  =  2.23 meters per second     

b)  888 cm  =  8.88 meters     

     8.88 meters / 4.88 sec  =  1.82 meters per second     

c)  2.23 m/s is greater than 1.82 m/s     

_.     

A school bought many boxes of 100 candies each. The teachers opened all the boxes and gave 14 candies to each student, with 12 candies leftover at the end. The receipt shows the school bought 10{*} boxes of candies where the units digit, represented by {*}, was covered by a chocolate smudge. How many boxes of candies did the school buy?     

One box of a 100 will serve 7 students at 14 candies each, with 2 left over.     

By the time the first 100 boxes have been distributed, there are 200 candies left over.     

That left over 200 is the same as 2 boxes, so after these are distributed there are 4 left over.    

We need to have a total of 12 candles left over so we need to add 8 more to the 4 we already have.    

Since 2 candies are left over from each boxful, we need 4 more boxes, making it 104 boxes in total.     

Check answer:     104 boxes equals 10,400 candies.     

                              Divided by 14 equals 742 Remainder 12     

_.    

suppose $125.00 is placed in a savings account for 2 years. find the amount of interest and the total amount if the account earned 4.5% during this time period     

Amount of Interest                      $125.00 x 4.5%  =     

                                                    $125.00 x 0.045  =  $5.625     

round to even number                                            =  $5.62     

Total Amount Now                      $125.00 + $5.62  =  $130.62     

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