ajit257 wrote:
Raymond purchased a package of ground beef at a cost of $1.98 per pound. If, for the same amount of money, Raymond could have purchased a piece of steak that weighed 40 percent less than the package of ground beef, what was the cost per pound of the steak?
A. $4.95
B. $4.20
C. $3.60
D. $3.30
E. $3.10[/quote
Fedemaravilla wrote:
I think this answer I bad written. It talks about a package of beef not specifing that how many pounds does it weight. Then it says again 40% less than the package, how can we assume that the package weights 1 pound??
Fedemaravilla , it might seem confusing, but you should not assume the first package weighs one pound. See
Bunuel ,
aboveYou are dealing with a rate (
\(\frac{cost}{pound}\)), not a quantity.
The prompt gives us "cost per [one] pound" for convenience.
But "cost per [one] pound" does not mean there is
only one pound.
Suppose the first package weighed two pounds.
The prompt would have told us it cost $3.96.
The rest of the question would be the same.
What was the cost per pound of the steak?
\(\frac{TotalCost}{NumberOfLbs}\) =
Cost per poundThe number of pounds changed to a fraction of the original number of pounds
40 percent less than 2 pounds = (.60)(2) = 1.2 pounds
The equation for the original
rate also must change:
From
\(\frac{$3.96}{2 lb}\) to
\(\frac{$3.96}{1.2lbs} = $3.30\) per pound for steak
Similarly, here:
\(\frac{$1.98}{1lb} = $1.98\) per pound for ground beef.
The number of pounds changed from 1 to 0.6 pounds
That changes the original rate
The equation also must change to
\(\frac{$1.98}{.60} = $3.30\) per pound of steak
In short, when you see "cost per pound," you are dealing with a rate, not a quantity.
Focus on the rate, and in this case, how the rate gets changed.
Hope that helps.