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# Help

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All sacks of sugar have the same weight. All sacks of flour also have the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that two sacks of sugar together with three sacks of flour weigh no more than 40 pounds, and that the weight of a sack of flour is no more than 5 pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?

The Highly Improbable Foods Company makes vegetarian versions of burgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of one burger, three hot dogs, and 5 chicken wings, which costs \$16. Platter B consists of two burgers, one hot dog, and 8 chicken wings, which costs \$20.

A picnic organizer requires 80 hamburgers, 95 hot dogs, and 380 chicken wings. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost (in dollars)?

Feb 5, 2020

#1
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I also need help on these problems:

A can do a work in 14 days and working together A and B can do the same work in 10 days. In what time can B alone do the work?

There are 40 pigs and chickens in a farmyard. Joseph counted 100 legs in all. How many pigs and how many chickens are there?

A health club charges a one-time initiation fee and a monthly fee. John paid 100 dollars for 2 months of membership. However, Peter paid 200 for 6 months of membership. How much will Sylvia pay for 1 year of membership?

The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that show how many times a week Madison eats breakfast.

A fruit basket contains the same number of apples and pears. If Eric eats 5 apples and 1 pear, there will be twice as many pears as apples. How many pears remain in the basket?

At 2:00 P.M. a train A leaves a station traveling at 100 mi/hr. At 4:30 P.M. train B leaves the station on a parallel route and traveling at 150 mi/hr. How far away from the station will the second train overtake the first train?

Feb 5, 2020
#2
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See detailed solution to your FIRST question here:  https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1076461.html

Feb 5, 2020
#3
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A can do a work in 14 days and working together A and B can do the same work in 10 days. In what time can B alone do the work?

We have   that  A  can do (1/14)  of the work in one day

And A and B  can do (1/10)  of the work each day

Let (1/x) be the fraction of the work that B can do in one day

So

(1/14)  +  1 / x =  1/10         subtract   1/14  from both sides

(1/10)  - (1/14) =  1/x

[14 - 10 ] / 140  =  1/x

4 / 140  =  1/x      and we can write

140 / 4  =  x

35   = x

So....it takes B 35 days to do the work alone

Feb 5, 2020
#4
+107011
+2

There are 40 pigs and chickens in a farmyard. Joseph counted 100 legs in all. How many pigs and how many chickens are there?

Let  x  be the number of chickens

Then 40 - x  =  the number of pigs

So

Legs per chicken * number of chickens  +  Legs per p*g * number of pigs  =  100

2x + 4(40 - x)  =  100   simplify

-2x + 160  = 100       subtract 160 from both sides

-2x = -60         divide both sides by -2

x = 30  = number of chickens

Feb 5, 2020
#5
+107011
+2

A fruit basket contains the same number of apples and pears. If Eric eats 5 apples and 1 pear, there will be twice as many pears as apples. How many pears remain in the basket?

Let x be the equal number of apples and pears....so

x - 1         2

____  =   ___              cross-multiply

x  - 5        1

1 ( x - 1)  = 2 ( x - 5)    simplify

x - 1 =  2x  - 10        add 10 to both sides, subtract x from both  sides

9  = x

The number of remaining pears =   x - 1  =  9  - 1   =  8

Feb 5, 2020
#6
+20216
+2

At 2:00 P.M. a train A leaves a station traveling at 100 mi/hr. At 4:30 P.M. train B leaves the station on a parallel route and traveling at 150 mi/hr. How far away from the station will the second train overtake the first train?

Train A has a 2  1/2 hour head start     2 1/2 hr  x 100 mph = 250 m   head start

Train B travels (150 - 100) m/hr =   50 m/hr faster

Start by finding how long it will take train B to cover the 250 mile gap at 50 m/hr

now you will know how long train B has been travelling when it catches train A

then  rate   x  time  = distance from station

150 m/r    x time = distance

You should at LEAST try to solve ALL of these before postin all of your homework.....If you cannot even attemp them, you are in a clas too far advanced for your knowledge level and should be getting some remedial education.....

THIS FORUM IS NOT FOR DOING YOUR HOMEWORK FOR YOU......sTOP BEING LAZY.   AT LEAST TRY !       THEN POST YOUR q'S

Feb 5, 2020
#7
+107011
+1

At 2:00 P.M. a train A leaves a station traveling at 100 mi/hr. At 4:30 P.M. train B leaves the station on a parallel route and traveling at 150 mi/hr. How far away from the station will the second train overtake the first train?

Let  H  be the number  of hours  that  train B travels

And the number of hours that train A travels = 2.5 + H

And   Rate * Time  = Distance Traveled

And when B catches A they will have traveled the same distance....so.....

100 (2.5 + H)  = 150 (H)    simplify

250 + 100H  = 150H          subtract 100H from both

250  = 50H             divide both sides by  50

5   = H

So.....train B catches A at  4:30 PM + 5 hrs  =    9:30 PM

Feb 5, 2020
#8
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...I wasn't the one who posted multiple questions after this, I only posted the two questions on the op.

Feb 5, 2020
#9
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But I do need help on the two on the original post...

Guest Feb 5, 2020
#10
+107011
+1

All sacks of sugar have the same weight. All sacks of flour also have the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that two sacks of sugar together with three sacks of flour weigh no more than 40 pounds, and that the weight of a sack of flour is no more than 5 pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?

Let the weight of  a sack of sugar  =  W

Let the weight of  a sack of flour  =  2W + 5

And we have that

2W  + 3 (2W + 5)  ≤ 40       simplify

2W  + 6W + 15 ≤  40

8W ≤  25      divide  both sides by  8

W ≤  25 / 8  =   3.125  lbs

So....the max weight for a sack of flour  =  8.125 lbs

Feb 5, 2020