He used 86 pounds of type A coffee.
Step-by-step explanation:
Cost of type A coffee = $5.40 per pound
Cost of type B coffee = $4.05 per pound
Total blend made = 138 pounds
Total cost = $675.00
Let,
x represents the pounds of type A coffee
y represents the pounds of type B coffee
According to given statement;
x+y=138 Eqn 1
5.40x+4.05y=675 Eqn 2
Multiplying Eqn 1 by 4.05
[tex]4.05(x+y=138)\\4.05x+4.05y=558.90\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5.40x+4.05y)-(4.05x+4.05y)=675-558.90\\5.40x+4.05y-4.05x-4.05y=116.1\\1.35x=116.1\\[/tex]
Dividing both sides by 1.35
[tex]\frac{1.35x}{1.35}=\frac{116.1}{1.35}\\x=86[/tex]
He used 86 pounds of type A coffee.
Keywords: linear equation, elimination method
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