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July 24th, 2015, 03:42 AM   #1
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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.
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July 24th, 2015, 05:58 AM   #2
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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.
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Last edited by skipjack; July 24th, 2015 at 01:35 PM.
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July 24th, 2015, 07:51 AM   #3
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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.
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July 25th, 2015, 05:01 AM   #4
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Country Boy and Benit 13, thank you very much for your explanation!
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