July 24th, 2015, 03:42 AM  #1 
Newbie Joined: Jul 2015 From: N/A Posts: 17 Thanks: 0  word problem
The question is "a steak costs \$4 more than a hamburger, and a hamburger costs \$4 more than a grilled cheese sandwich. If 6 grilled cheese sandwiches cost 2x dollars, how much will 4 steaks and 2 hamburgers cost?" The answers are A) 2x+40 B) 2x+48 C) 6x+34 D) 12x+40 Last edited by skipjack; July 24th, 2015 at 01:34 PM. 
July 24th, 2015, 05:58 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Let "C" be the cost of a grilled cheese sandwich. "A hamburger costs 4 more than a grilled cheese sandwich" so a hamburger costs C+ 4. "A steak costs 4 more than a hamburger" so a steak cost (C+ 4)+ 4= C+ 8. "If 6 grilled cheese sandwiches cost 2x dollars" then 6C= 2x so C= 2x/6= x/3. "how much will 4 steaks and 2 hamburgers cost?" One steak cost C+ 8 so 4 steaks cost 4(C+ 8)= 4C+ 32. One hamburger cost C+ 4 so 2 hamburgers cost 2(C+ 4)= 2C+ 8. Together that would be 4C+ 32+ 2C+ 8= 6C+ 40. Since C= x/3, 4 steaks and 2 hamburgers cost 6(x/3)+ 40= 2x+ 40. Last edited by skipjack; July 24th, 2015 at 01:35 PM. 
July 24th, 2015, 07:51 AM  #3 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Nice answer! That's how I'd normally answer it. Here's another way... Let's identify a couple of things: 1. If we compare the number of grilled cheese sandwiches with which the cost is known and the number of hamburgers and steaks we are buying, the numbers are the same (6). 2. The changes in price between the items are purely additive. Based on the two points above, we can deduce that cost for 4 steaks and 2 hamburgers = cost for 6 grilled cheese sandwiches + extra amount Extra amount = (4) $\displaystyle \times$ number of hamburgers + (4+4) $\displaystyle \times$ number of steaks = $\displaystyle 4 \times 2 + 8 \times 4$ = 8 + 32 = 40 Therefore, the cost for the 4 steaks and 2 hamburgers is 2x + 40. 
July 25th, 2015, 05:01 AM  #4 
Newbie Joined: Jul 2015 From: N/A Posts: 17 Thanks: 0 
Country Boy and Benit 13, thank you very much for your explanation!


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