CPM Homework Help : A2C Problem 11-89

Betty's Quick Stop makes a $15\%$ profit on its lunches and a $22\%$ profit on its dinners. If Betty took in $$2700$ on Tuesday and made $$513.01$ profit, how much did Betty take in on lunch? Write one or two equations, then solve.

Step 1:

Set up a system of equations.
Make x = lunch and y = dinner.

$x + y = 2700$
$15x + 22y = 51,301$

Step 2:

Set the equation like a mixture problem.

$15x + 22\left(2700 − x\right) = 51,301$

Step 3:

Distribute.

$15x + 59,400 − 22x = 51,301$

Step 4:

Solve for x.

$7x = 8099$

Answer:

$x = $1157$