Bosco

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?  

Same team, same speed, same paint, but three times as much wall.  

Therefore, it'd take three times as much time:   3 * 40 min  =  120 min  

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One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?  

To find b, consider                                                  ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

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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 start with 200 kg of berries, and 99% of that is water.  

Since they're 99% water, that means that there is 1% of solid stuff.  

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

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

So there still remains 2 kg of solid stuff.  

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

So 2 kg (the solid stuff) is 10% of the total weight.  

That means the new total weight is 20 kg.  

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>>>>> and it was taken down <<<<<  

Are you certain?  Is it possible that so many new postings came in during those couple of days that your posting just got pushed down off the top page?  Maybe several pages down.  If you'd register an account, you could click your user name and get to a compilation of every thing you had posted under that username.     

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Will and Grace are canoeing on a lake.  Will rows at 50 meters per minute and Grace rows at 20 meters per minute. Will starts rowing at 2 p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at 2 p.m. If they always row directly towards each other, and the lake is 3800 meters across from the west side of the lake to the east side, at what time will the two meet?  

Will's rate is 50 m/min.  

Grace's rate is 20 m/min.  

They're rowing toward each other,  

so their rate of closure is 70 m/min.  

The lake is 3800 meters across.  

The time it will take them to meet is given by  

                                                                                    Distance  

                                                                            T  =  –––––––  

                                                                                       Rate  

                                                                                    3800 m  

                                                                            T  =  –––––––  

                                                                                    70 m/min  

The time it takes them to meet                             T  =  54.29 min  

The time on the clock is          2:00 pm + 54.29 min  =  2:54:17 pm 

(The :17 is because 0.29 minute is 17 seconds.)  

A bag contains yellow, green, blue, and white marbles.  The ratio of yellow, green, blue, and white marbles is 1:2:3:4.  If the bag contains 180 marbles, then how many blue marbles are there?  

Consider:  "The ratio of yellow, green, blue, and white marbles is 1:2:3:4."  

Call the number of yellow marbles X.  

So the number of green marbles is 2X. 

And the number of blue marbles is 3X.  

And the number of white marbles is 4X.  

Add up all the marbles and you have     10X  =  180  

Therefore                                                   X  =  18 yellow marbles  

                                                                 2X  =  36 green marbles  

                                                                 3X  =  54 blue marbles  

                                                                 4X  =  72 white marbles  

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Hello Monica.  Good work.  Excellent, even :-)   When I answered this same problem some time back, I took a slightly different path, but we both ended up at the same place, namely 104 gallons of paint.  I was happy to see someone else's answer was consistent with mine, because there was a "solution" even earlier than mine that ended with a different (read incorrect) answer.  Here's how I did it:    

You're going to have to convert those meters to square feet,  

so I think it's better to do it from the start.  Even though we'll  

have fractions to contend with, a calculator makes that easy.  

                                                                       12 m  

1 foot is 0.3048 meter, so the height is       –––––––––  =  39.3701 ft   

                                                                   0.3048 m/ft  

                                                                       120 m  

1 foot is 0.3048 meter, so the length is       –––––––––  =  393.7007 ft   

                                                                   0.3048 m/ft  

Area is height times length     (39.3701 ft)(393.7007 ft)  =  15,500.0359 sq ft  

1 gallon will cover 150 sq ft  

so divide that into the area               15,500.0359 sq ft  

                                                        –––––––––––––––  =  103.3335 gallons  

                                                           150 sq ft/gallon  

You can't buy just part of a gallon of paint,  

so we have to round that up to whole gallons                       104 gallons  

_.

Solve 3a + 4b = 5a - 6b + 24 - 3a for a in terms of b.  

                                                            3a + 4b  =  5a – 6b + 24 – 3a   

You just add up the like terms.  

                                                            3a + 4b  =  2a – 6b + 24  

And subtract 2a from both sides  

                                                              a + 4b  =  – 6b + 24  

And subtract 4b from both sides  

                                                                      a  =  – 10b + 24  

When you get better at it, you  

can combine simple steps like  

addition/subtraction of terms.  

It's conventional to place the  

positive number ahead of the  

negative number.  

                                                                       a  =  24 – 10b  

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In regard to #1 above "...the value of k that makes the equation have exactly one solution is k = 3/2."  

I think that solution was for the value of x, instead of for the value of k.  

I followed as far as "...one solution when the discriminant b^2 - 4ac = 0."  So far, so good. 
 

At that point, I think I would substitute values in             b² – 4ac  =  0  

                                                                            (6)² – (4)(2)(k)  =  0  

                                                                                        36 – 8k  =  0  

                                                                                                8k  =  36  

                                                                                                  k  =  36/8  

                                                                                                  k  =  9/2  

I don't know how to check the veracity  

of this answer.  If I'm wrong, I would truly  

appreciate someone showing me where.  

_.