A problem by Raven Carl Uyanguren

Level pending

Patrick bought 50 pounds of meat consisting of hamburger and steak. Steak costs twice in much per as hamburger. If he bought $30 worth of burger and $90 worth of steak, then how many pounds of each did he buy?

10 pounds of burger and 15 pounds of steak 30 pounnds of burger and 30 pounds of steak 25 pounds of burger and 20 pounds of steak 20 pounds of burger and 30 pounds of steak

Raven Carl Uyanguren by Raven Carl Uyanguren , 31, Philippines

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2 solutions

Som Ghosh
Jul 17, 2015

Your options are really weird, only one option which will add up to 50 pound.

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this is the first time for me to post a question :D I'm trying if someone will really answer it:D i answered the question and put random choices :D

Raven Carl Uyanguren - 5 years, 11 months ago
Chew-Seong Cheong
Jul 17, 2015

Let the weights of burger and steak be x x and y y pounds respectively. Then we have:

{ x + y = 50 . . . ( 1 ) 30 x × 2 = 90 y ⇒ y = 3 2 x . . . ( 2 ) \begin{cases} x + y = 50 & &...(1) \\ \dfrac{30}{x} \times 2 = \dfrac{90}{y} & \Rightarrow y = \dfrac{3}{2} x & ...(2) \end{cases}

( 1 ) : x + 3 2 x = 50 ⇒ x = 20 ⇒ y = 30 \begin{aligned} (1): \quad x + \dfrac{3}{2}x & = 50 \quad \Rightarrow x = \boxed{20} \quad \Rightarrow y = \boxed{30} \end{aligned}

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