Answer to Question #187198 in Algebra for Marushka Moonsamy

Question

Three students, A, B and C, received a Stadio Mathematics award for their top performance. They have decided to split the award as follows: i. Student A receives R10 000 plus 1 5 of what then remains; ii. Student B then receives R16 000 plus 1 4 of what then remains; and iii. Student C then receives the rest, which is R18 000. How much is the original monetary award? Which student receives the most money?

Answer 1

Let original monetary award be x

Student A receives 10,000 and $\frac{1}{5}$ of remaining

$A=10,000+\frac{1}{5}(X-10,000)........(i)$

Student B receives 16,000 and $\frac{1}{4}$ of remaining

$B=16,000+\frac{1}{4}(X-16,000-A).....(ii)$

Student C receives the rest which is 18000

$X-A-B=18,000.......(iii)$

From (i)(ii)(iii)

$=X-[10,000+\frac{1}{5}(X-10,000)]-[16,000+\frac{1}{4}(X-16,000-A)]=18000$

$=X-8000-\frac{1}{5}X-12000-\frac{1}{4}X+\frac{A}{4}=18000$

$=X-8000-\frac{1}{5}X-12000-\frac{1}{4}X+\frac{1}{4}(8000+\frac{1}{5}X)=18000$

$=\frac{12}{20}X=18000+18000$

$X=60,000$

$R 60,000$ is the original monetary award.

Student A $=10,000+\frac{1}{5}×(60000-10000)$

$=R 20000$

Student B

$=16000+\frac{1}{4}×(60000-16000-20000)$

$=R 22000$

Student C

$=R 18000$

Student B receives the most money.