Answer
One pound of the 90% lean ground beef costs 3 dollars and one pound of the 80% lean ground beef costs 2.4 dollars.
Work Step by Step
We assign the variables:
x = price of the 90% lean ground beef
y = price of the 80% lean ground beef
Step 1:
Find the equations that represent the problem.
We can get the first equation from the wording in the problem.
From " Ground beef that is 90% lean costs 1 1/4 times the cost of 80% lean ground beef", we get:
$x=1\frac{1}{4}y$ Remember $1\frac{1}{4}=1.25$, so
$x=1.25y$ -> Eq. 1
We can get the second equation from the wording in the problem.
From "the total cost of one pound of 90% lean ground beef plus one pound of 80% lean ground beef is 5.40 dollars", we get:
$x+y=5.4$ -> Eq. 2
Step 2:
Solve the system of equations using the substitution method,
-> Substitute Eq. 1 into Eq. 2
$1.25y+y=5.4$
$2.25y=5.4$
$y=\frac{5.4}{2.25}$
$y=2.4$
-> Substitute the value for $y$ into Eq. 1
$x=1.25(2.4)$
$x=3$
Step 3:
One pound of the 90% lean ground beef costs 3 dollars and one pound of the 80% lean ground beef costs 2.4 dollars.
