Bosco

There are 70 cookies in a box. The number of raisin cookies was 1/4 the number of plain cookies. Josephine ate 3 raisin cookies and 3 plain cookies. Find the difference between the number of raisin and plain cookies in the box in the end.     

Consider the ratio 1/4.     

That is, for every 5 cookies, 1 is a raisin and 4 are plain.     

So divide 5 into 70 to get 14 ... let's call them "portions".     

The raisin cookies get 1 portion, so there are 14 of them.     

The plain cookies get 4 portions, so there are 56 of them.     

The difference in the number of cookies is (56 – 14) = 42      

So, as long as Josephine eats the same number of raisin cookies     

as she eats plain cookies, the difference will always be 42 cookies.     

_.     

Your weekly paycheck is 10 percent less than your coworker's. Your two paychecks total 780. Find the amount of each paycheck.     
Your coworker's:                and your's:     

Your two paychecks total 780, so Yours = 390 ... i.e., half of 780.     

Then, 390 = 0.90 • CoWorker's     ——>>     CoWorker's = 390 / 0.90     

                                                                       CoWorker's = 433.33     

_.     

There are 60 cookies in a box. The number of raisin cookies was 1/3 the number of plain cookies. Rose ate an equal number of raisin and plain cookies. Find the difference between the number of raisin and plain cookies in the end.    

1. Consider the Raisin being 1/3 the number of Plain.     

2. That means for every 4 cookies, 1 is Raisin and 3 are Plain.     

    Restate line 2 but multiply everything by 15.     

3. That means for every 60 cookies, 15 are Raisin and 45 are Plain.     

So, the difference between the Raisin and Plain cookies is 45 – 15 = 30.     

As long as Rose eats an equal number of Raisin and Plain cookies,     

the difference between the two kinds will always be 30 cookies.     

_.     

Math club is having a fund-raising event at the Atlantis Resort. The resort is charging $2000 for the room and $50 additional for each guest in attendance. If 1000 guests attend the event, what was the total revenue to ensure $10000 in profits.     

Expenses:                            $  2,000     

                      $50 x 1,000 = $50,000     

total expenses                      $52,000     

Want to make $10,000 profit     

break even point                   $52,000     

profit                                      $10,000     

add together                          $62,000     

The sponsors need to gross $62,000 to pay $52,000 for the hall and realize $10,000 profit.     

This does not take into account expenses other than renting the hall, such as refreshments.     

_.     

There are 8 sixth-graders and 16 seventh-graders in a class.     

Complete the ratio for this class.     

Enter the correct answer in the box.     

1 out of every  students is a sixth-grader.     

I assume the box is between "every" and "student" in the last line.     

There are 24 students, 8 of them are sixth graders,     

therefore 1 out of every 3 students is a sixth grader.     

_.    

The ratio of Alan's apples to Don's apples was 3:5. When Alan gave 30 of his apples to Don, the ratio of Alan's apples to Don's apples became 1:5. Find the number of apples Alan had at first?     

A / D  =  3 / 5                      crossmultiply ——>>  5A  =  3D     

(A–30) / (D+30)  =  1 / 5     crossmultiply ——>>  5 • (A–30)  =  1 • (D+30)     

5A – 150  =  D + 30     

from (eq 1) 5A = 3D    substitute this into the previous      

3D – 150  =  D + 30     

          2D  =  180     

            D  =  90     

          5A  =  3D     

          5A  =  3 • 90     

          5A  =  270     

            A  =  54     

_.     

Jeremy is twice as old Randy now. 6 years ago, the sum of their age was 18. How old is Jeremy now?     

J  =  2R                            (eq 1)     

(J – 6) + (R – 6)  =  18     (eq 2)     

substitute 2R wherever you see J in (equation 2)     

(2R – 6) + (R – 6)  =  18     

     2R – 6 + R – 6  =  18     

                3R – 12  =  18     

                        3R  =  30     

                          R  =  10     

from (eq 1)         J  =  2R    

                           J  =  2 • 10     

                           J  =  20     

_.     

Kaden is 1/4 as old as Tom now. In 7 years, the sum of their age will be 54. How old is Tom now?     

K  =  (1/4) T     ——>>  T  = 4 K    (eq 1)     

(K + 7)  +  (T + 7)  =  54                (eq 2)     

sub (eq 1) into (eq 2)        (K+7) + (4K+7)  =  54     

                                                     5K + 14  =  54     

                                                              5K  = 40     

                                                                K  =  8     

                                                                T  =  4K     

                                                                T  =  4 • 8     

                                                                T  =  32     

_.     

You take the four Aces, four 2's, and four 3's from a standard deck of 52 cards, forming a set of 12 cards. You then draw three cards at random.  What is the probability that you get an Ace, a 2, and a 3?     

First card can be anything                            probability 12 / 12 or 1 / 1     

For example only, say it's a 2     

Second card can one of the     

remaining eight appropriate cards                 probability 8 / 11     

For example only, either a A or a 3,     

so let's just say it's an Ace     

Third card must be one of the     

remaining four appropriate cards                   probability 4 / 10     

For example only, it has to be a 3     

Probability of all three happening,     

multiply the individual probabilities                 (1/1) • (8/11) • (4/10)  =  32/110   

                                                                        32/110     reduces to     16 / 55     

_.     

Suppose a model of the Olympic rings is constructed and each circle has a radius of 6 feet. What is the amount of rope used in the construction of the model of five rings? Explain how you solved the problem. Use 3.14 for π. Round to the nearest hundredth, if necessary.     

There are five rings, or circles, so you have to find the total of the circumferences of all of them.     

C =  π d     

C = 3.14 • 12 ft     

C = 37.68 ft           that's one circle     

Total = 5 • 37.68 ft =  188.40 ft     

_.     

x/y = 1/4     

x/(16+y) = 3/14    

x/y = 1/4              crossmultiply   ———>>  4x = y     

x/(16+y) = 3/14   crossmultiply   ———>>  14x = 48+3y     

                            14x = 48 + 3y     

                            14x = 48 + (3)(4x)     

                            14x = 48 + 12x     

                              2x = 48     

                                x = 24     

                               4x = y     

                                 y = 4x = (4)(24)     

                                 y = 96     

_.