Boris's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs boris $5.45 per pound, and type b coffee costs $4.20 per pound. this month, boris made 178 pounds of the blend, for a total cost of $870.10 . how many pounds of type b coffee did he use?

X=pounds of Type A coffee
y=pounds of Type B coffee

QUANTITY EQUATION:
x+y=178

COST EQUATION:
$5.45x + $4.20y=$870.10

STEP 1:
Solve for one variable in equation one.  Then substitute it in equation two.

x+y=178
subtract y from both sides of the equation
x=178-y

STEP 2:
substitute x=178-y in equation two

5.45x + 4.20y=870.10
5.45(178-y) + 4.20y=870.10
multiply 5.45 by everything in parentheses

(5.45*178)+(5.45*-y)+4.20y=870.10
970.10-5.45y+4.20y=870.10
combine like terms

970.10-1.25y=870.10
subtract 970.10 from both sides

-1.25y=-100
divide both sides by -1.25

y=80 pounds of type B coffee

STEP 3:
Substitute y=80 in either equation to solve for x

x+y=178
x+80=178
subtract 80 from both sides
x=98 pounds of type A coffee

ANSWER:
x=98 pounds of type A coffee
y= 80 pounds of type B coffee

CHECK:
Substitute answers for x & y into either equation to be sure it checks.

5.45x+4.20y=870.10
5.45(98)+4.20(80)=870.10
534.10+336=870.10
870.10=870.10

Hope this helps!  :)

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Step-by-step explanation: