Please explain how to do these using equations?

Question

a) The length of a rectangle is 5m shorter than three times the width. If the perimeter is 54m, what are the dimensions of the rectangle?

b) Helen goes by bus or part of the way to school and runs the rest. If the time spent on running is 3 minutes longer than that on taking the bus and the total time spent is 15 minutes, how long does she spend on taking the bus?

c) $3000 is divided between two sons so that the elder son receives $200 more than two thirds the share of the younger son. How much does each receive?

d) May has 80 coins which of 10 cents coins, 20 cent coins and $1 coins. Among the coins, there are 4 more $1 coins than 10 cent coins and 6 more 20 cents coins than $1 coins. How much money does she have?

Please show working in equations and explain thanks.

Answer 1

a) First guy is correct

b) run = bus+3, bus+bus+3 = 15, bus *2 = (15-3) = 12, bus = 12/2 = 6.

c) (2/3 share) + (share) = 3000 - 200
2800 = (5/3 * share)
share = 2800*3 / 5 = 8400 / 5 = 1680
elder son gets 200 + (2/3 * 1680) = 200+ 1120 = 1320

d) 80 coins = (x 10c coins) + (x+4 $1 coins) + (x+4+6 20c coins)
80 = y + y+4 + y+4+6
80 = 3y + 4 + 4+ 6
80 = 3y + 14
3y = 80-14 = 66
y = 66/3 = 22

Therefore 22 10c coins, 26 $1 coins and 32 20c coins
(22 x 0.10) + (26 x 1) + (32 x 0.20) =
2.20 + 26.00 + 6.40 = 34.60

Answer 2

L = 3 W - 5 . . . substitute this to the next equation
54 = 2(L + w)
54 = 2(3w - 5 + w) = 2 (4w - 5) = 8w - 10
8w = 64
w = 8
L = 24 - 5 = 19

let t = time consumed in bus
15 - t = time consumed in running
15 - t = t + 3
2t = 12
t = 6 minutes. . . time using bus
15 - t = 9 minutes. . . time in running

let d = $1 . . . . t = 10 cents . . . . . w = 20 cents
d = t + 4 . . . . equation 1
w = d + 6 . . . equation 2
d + t + w = 80 . . equation 3 . .. substitute d of equation 1
. . . . . . . . to equation 2 and equation 3
w = t+ 4 + 6 . . . . from equation 2
w = t + 10 . . . . .this is equation 4
t + 4 + t + w = 80
w = 76 - 2t . . . . equation 5 . . . . . . equate EQ4 and EQ5
t + 10 = 76 - 2t
3t = 66
t = 22 . . pieces of 10 cents coins
w = t+10 = 32 . . pieces of 20 cents coins
d = t + 4 = 26 . . . pieces of $1 coins
total coins = 22 + 32 + 26 = 80 coins

Answer 3

Perimeter formula

P = 2L + 2W

let

w = width

3w - 5 = length

54 = Perimeter

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The equation

54 = 2(3w - 5) + 2w

The distributive propertyy

54 = 6w - 10 + 2w

Collect like terma

54 = 8w - 10

Transpose 10

54 + 10 = 8w - 10 + 10

Collect like terms

64 = 8w

Divide both sides of the equation by 8

64 / 8 = 8w / 8

64/8 = w

8 = w. . .The width

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The width is 8 m

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The length is 3w - 5

3(8) - 5 =

24 - 5 =

19

The length is 19 m

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Answer 4

Algebra!
a)
l=3w-5(1)
2w+2l=54(2)
(1) in (2):
2w+6w-10=54
8w-10=54
8w=44
w=5.5
l=11.5

b)
12mins
Though the grammar is terrible and the question is hard to follow.

c)
3000=e+y(1)
e=2y/3+200(2)
(2) in (1)
3000=2y/3+200+y
2800=5y/3
e=1680, y=3000-1680=1320

d)
a=b+4
c=a+6
a+b+c=80
b+4+b+a+6=80
2b+10+b+4=80
3b+14=80
3b=66
b=22
a=26
c=32
1*26+0.1*22+0.2*32
=$34.6