SOLUTION: An amount of Rs. 8750 is made up with the notes of denominations Rs. 100, 50, 20, and 10. The number of Rs. 10 notes are 4 times the number of Rs. 20 notes. The number of Rs. 20 no

Question 1077739: An amount of Rs. 8750 is made up with the notes of denominations Rs. 100, 50, 20, and 10. The number of Rs. 10 notes are 4 times the number of Rs. 20 notes. The number of Rs. 20 notes are 3 times the number of Rs. 50 notes. The number of Rs. 50 notes are 5 times the number of Rs. 100 notes. How many total notes of denomination Rs. 100 are there?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let a = number of 100 rs notes.
let b = number of 50 rs notes.
let c = number of 20 rs notes.
let d= number of 10 rs notes.

d = 4c (number of 10 rs notes = 4 * number of 20 rs notes)
c = 3b (number of 20 rs notes = 3 * number of 50 rs notes)
b = 5a (number of 50 rs notes =5 * number of 100 rs notes)

your equation is 100a + 50b + 20c + 10d = 8750

replace d with 4c and the equation becomes 100a + 50b + 20c + 10*4c = 8750

simplify to get 100a +50b + 20c + 40c = 8750

combine like terms to get 100a + 50b + 60c = 8750

replace c with 3b to get 100a + 50b + 60*3b = 8750

simplify to get 100a + 50b + 180b = 8750

combine like terms to get 100a + 230b = 8750

replace b with 5a to get 100a + 230*5a = 8750

simplify to get 100a + 1150a = 8750

combine like terms to get 1250a = 8750

solve for a to get a = 8750 / 1250 = 7

you were given:

d = 4c (number of 10 rs notes = 4 * number of 20 rs notes)
c =3b (number of 20rs notes = 3 * number of 50 rs notes)
b = 5a (number of 50 rs notes = 5 * number of 100 rs notes)

based on that, you can calculate:

a = 7
b = 5 * 7 = 35
c = 3 * 35 = 105
d = 5 * 105 = 420

you have:

a = 7
b = 35
c = 105
d = 420

your original equation was 100a + 50b + 20c + 10d = 8750

replace all the variable with their values to get:

100*7 + 50*35 + 20*105 + 10*420 = 8750

simplify to get:

700 + 1750 + 2100 + 4200 = 8750

combine like terms to get 8750 = 8750

since this is true, then your values for each of the variables involved is correct.

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