Answer :
Mary used 96 pounds of type b coffee this month.
Using algebraic expression and equation, we can solve how much of each type of coffee did Mary used that month.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Given that that month, Mary made 181 pounds of the blend that is a mixture of two types of coffee, we can express this as:
181 = a + b
where a = pounds of type a coffee that costs $5.35 per pound
b = pounds of type b coffee that costs $4.15 per pound
Also, the total cost of the blend that month is $853.15, which is the sum of the total cost of the two types of coffee. We can express that as:
$853.15 = $5.35(a) + $4.15(b)
Using substitution method to solve the two equations,
181 = a + b ⇒ a = 181 - b
$853.15 = $5.35(181 - b) + $4.15(b)
853.15 = 968.35 - 5.35b + 4.15b
5.35b - 4.15b = 968.35 - 853.15
1.2b = 115.2
b = 96
a = 181 - b
a = 181 - 96
a = 85
Hence, Mary used 85 pounds of type a coffee and 96 pounds of type b coffee that month.
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