Systems of Linear Equations problem solving Help?

Question

Even just help on figuring out the working equations will do, thank you.

1. The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 2200 people entered the park, and the admission fees collected totaled $5050. How many children and how many adults were admitted?

2. A boat on a river travels downstream between two points, 20 mi apart, in one hour. The return trip against the current takes 2 and 1/2 hours. What is the boat's speed, and how fast does the current in the river flow.

3. A biologist has two brine solutions, one containing 5% salt and another containing 20% salt. How many milliliters of each solution should he mix to obtain 1 L of a solution that contains 14% salt?

4. A customer in a coffee shop purchases a blend of two coffees, Kenyan, costing $3.50 a pound, and Sri Lankan, costing $5.60 a pound. He buys 3 lb of the blend, which costs him $11.55. How many pounds of each kind went into mixture?

Answer 1

Q1)

5050 equals x number of children and y number of adults

x children and y adults equals 2200 so we can do simultaneous equations

5050=x1.5+y4  (a)

2200=x+y        (b)

(b)x4=

8800=4x+4y

(b)-(a)=

8800=4x+4y     (b)

5050=1.5x+4y  (a)

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3750=2.5x

3750/2.5=1500

so there's 1500 children

2200-1500=700

so 700 adults

Q2)

b+c=20

b-c=8

2b=28

b=14

c=6

yeah sorry i was wrong well done Catenary

Q3)

600ml of 20% solution = 120ml of salt

400ml of   5% solution =   20ml of salt

--------                                 ---------

1000ml                              140ml

=14% salt content

Q4)

11.55=5.6x+3.5y  (a)

3=x+y                     (b)

16.8=5.6x+5.6y    (b)

(b)-(a)=

5.25=2.1y

5.25/2.1=2.5

so 2.5 lbs of kenyan

and 0.5 lbs of sri lankan

Answer 2

C + A = 2200    (A = 2200 - C)

1.5C + 4A = 5050

Substitute 2200 - C for A in the second equation to obtain

1.5C + 8800 -4C = 5050

-2.5C = -3750

C = 1500

A = 2200 - 1500 = 700

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Going downstream the boat travels 20 mph

Going upstream the boat travels 20/2.5 = 8 mph

Assume the boat travels the same speed "x" with respect to the water

and the current is "y".

x + y = 20

x - y = 8

In this case lets add the two equations together

2x = 28

x = 14

y = 6

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0.05x + 0.20(1000 - x) = 0.14*1000

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3.5x + 5.6(3-x) = 11.55