# 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?

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

 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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