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To find the value of a quantity given ratio and the sum of the two quantities

by Yong Syafiqa Bte. Zainul Mujahidin
(Selangor,Taman Suntex,Malaysia)










































brian and mahmud won a contest.they shared prize of RM45000 in the ratio of 4:5.if brian receice the smaller share,how much did mahmud get?


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Apr 17, 2012
Value of a quantity given ratio and the sum of the two quantities
by: Staff


Question:


by Yong Syafiqa Bte. Zainul Mujahidin
(Selangor, Taman Suntex, Malaysia)


brian and mahmud won a contest.they shared prize of RM45000 in the ratio of 4:5.if brian receice the smaller share,how much did mahmud get?


Answer:

The two facts known about the contest are:

(Amount Received by Brian) + (Amount Received by Mahmud) = RM45000

(Amount Received by Brian)/(Amount Received by Mahmud) = 4:5 = 4/5

You have two equations with two unknowns.


To solve for Muhmud’s share, solve the second equation for Brian’s share, and then substitute that solution into the first equation.


2nd equation
---------------

(Amount Received by Brian)/(Amount Received by Mahmud) = 4/5


Multiply each side of the equation by (Amount Received by Mahmud)


[(Amount Received by Brian)/(Amount Received by Mahmud)]* (Amount Received by Mahmud) = (4/5)*(Amount Received by Mahmud)

(Amount Received by Brian) * [(Amount Received by Mahmud)/(Amount Received by Mahmud)] = (4/5)*(Amount Received by Mahmud)

(Amount Received by Brian) * 1 = (4/5)*(Amount Received by Mahmud)

(Amount Received by Brian) = (4/5)*(Amount Received by Mahmud)



1st equation
---------------

(Amount Received by Brian) + (Amount Received by Mahmud) = RM45000


Substitute the solution for the 2nd equation (above) into the first equation.

(Amount Received by Brian) = (4/5)*(Amount Received by Mahmud)


(Amount Received by Brian) + (Amount Received by Mahmud) = RM45000

(4/5)*(Amount Received by Mahmud) + (Amount Received by Mahmud) = RM45000


Combine like terms

(1+4/5)*(Amount Received by Mahmud) = RM45000

(9/5)*(Amount Received by Mahmud) = RM45000


Multiply each side of the equation by 5/9


(5/9)* (9/5)*(Amount Received by Mahmud) = (5/9) * RM45000

(9/9)* (5/5)*(Amount Received by Mahmud) = (5/9) * RM45000

(1)* (1)*(Amount Received by Mahmud) = (5/9) * RM45000

(Amount Received by Mahmud) = (5/9) * RM45000

(Amount Received by Mahmud) = RM25000


>>> the final answer: Mahmud = RM25000



Thanks for writing.

Staff
www.solving-math-problems.com



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