I need a step by step explanation for this maths problem, please. Have to use linear equation in one variable

Question

1)A total of Rs 50000 is to be distributed amongst 200 persons as prizes. A prize is either Rs 500 or Rs 200. Find the number of each type of prize.

2)Bryan left one fifth of his property for his son , one fifth for his daughetr and remainder for his wife. If his wife share was worth Rs 288000, find the total worth of Bryan's property.

Answer 1

1) let x be the number of Rs 500
so, 200 - x is the number of Rs 200 (because the number of prizes must sum up to 200 to be distributed amongst the 200 persons)

Rs 500*(number of Rs 500) + Rs 200*(number of Rs 200) = Rs 50000
(Rs 500)(x) + (Rs 200)(200-x) = Rs 50000
500x + 40000 - 200x = 50000 (just distributed Rs 200)
500x - 200x = 50000 - 40000 (40000 was subtracted from both sides of the equation)
300x = 10000
x = 33.3333 <--- number of Rs 500
200 - x = 166.666667 <--- number of Rs 200
the answers must be whole numbers... but if you will round it off to the nearest unit digit, there will only be a total of Rs 49900. so, it is not possible for 200 Rs 50000 to exist consisting only of either Rs 500 or Rs 200.

2) let x be the worth of Bryan's property
(Son's share) + (Daughter's share) + (Wife's share) = (total worth of Bryan's property)
(1/5)(x) + (1/5)(x) + Rs 288000 = x
(2/5)(x) + Rs 288000 = x
Rs 288000 = x - (2/5)(x)
Rs 288000 = (3/5)(x) (multiplying both sides of the equation by 5/3)
Rs 480000 = x

so, Bryan's property is worth Rs 480000

Answer 2

1) Let there be n prizes of Rs 500.
Therefore there are (200 - n) prizes of Rs 200

So n x Rs 500 + (200 - n) x Rs 200 = Rs 50000
So 500n + 40000 - 200n = 50000
So 300n = 10000
n = 33(and 1/3) So (200 - n) = 166 (and 2/3)

ie there are 33 prizes of Rs 500, 67 prizes of Rs 200 and there is Rs 100 left over (for expenses)

2) Let value of property be Rs P
Then son and daughter each gets Rs P/5 Total = Rs 2P/5
Thus his wife's share = Rs 3P/5
So 3P/5 = 288000
So 3P = 288000 x 5
P = 28800 x 5/3
= 96000 x 5
= 480000
So Bryan's property was worth Rs 480000

Answer 3

1) now, the total amount is 50000/-. it has to be distributed among 200 persons as prizes.
let the no. of persons who get the 500/- prize be x
let the no. of persons who get the 200/- prize be y
we know that total no. of persons is 200
so, x+y=200----(1)
and also, the total amount is 50000/-
so, x*500+y*200=50000---------(2)

solving (1) and (2), we get
x=166 and y=34

2) let the total property be x
his son's share is x/5
his daughter's share is x/5
his wife's share =x-(x/5+x/5)
=x-2x/5=3x/5
given that his wife's share is 288000/-
so, 3x/5=288000
simplifying, x=480000/-
so, bryan's total property is worth Rs 480000

Answer 4

Answer 2:
Let Bryan's property = 'x'
x = x/5 + x/5 + 3x/5
where 3x/5 is wife's share.
3x/5 = 288000
3x = 288000*5
3x = 1440000
x = 1440000/3
x = 480000
Bryan's property was worth Rs. 480000

Answer 5

First assign the variables Let x = the amount of 20% solution needed Let y = the amount of 50% solution needed Since there will be a total of 12 liters, you know that x + y = 12 Since you know that 20% of the x amount plus 50% of the y amount will equal 30% of the 12 liters. 0.2x + 0.5y = 0.3*12 Now, you multiply the 0.3*12, multiply the entire equation by 10 to clear the decimals, and you have a system of equations. x + y = 12 2x + 5y = 36

Answer 6

200x+500y=50000
reducing dividing by 100
2x+5y=500
x+y=200
multiplying the 2nd eqn. by 2
2x+2y=400
subtracting from eqn.1
3y=100
it gives y in fractions
will you check the sum and my calculations too

2.the fraction left to hiswife=1-(1/5)-(1/5)=3/5
3/5 corresponds to 288000
the entire property=288000*(5/3)
=Rs.480000