Question

equations and inequalities
solving a value mixture problem using a linear equation
reys coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs trey $4.20 per pound, and type b coffee costs $5.85 per p
his months blend used twice as many pounds of type b coffee as type a, for a total cost of $413.40. how many pounds of type a coffee were used?
number of pounds of type a coffee:

Explanation:

Step1: Define variables for coffee amounts

Let $x$ = pounds of type A coffee. Then $2x$ = pounds of type B coffee.

Step2: Set up total cost equation

Cost of A + Cost of B = Total cost:
$\$4.20x + \$5.85(2x) = \$413.40$

Step3: Simplify the left-hand side

Calculate the term for type B:
$4.20x + 11.70x = 413.40$
Combine like terms:
$15.90x = 413.40$

Step4: Solve for $x$

Divide both sides by 15.90:
$x = \frac{413.40}{15.90}$

Answer:

32