Question 1162586
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make a mixture of 12 pounds of tea worth $1.20 per pound by mixing tea worth $1.00 per pound with tea worth $1.30 per pound. What part of the mixture will be made up of the less expensive grade?
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make a mixture of P pounds of tea worth $T per pound by mixing tea worth $L per pound with tea worth $H per pound. What part of the mixture will be made up of the less expensive grade, the $L per pound?
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x of the less expensive grade
P-x of the other grade

{{{Lx+H(P-x)=TP}}}
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{{{Lx+HP-Hx=TP}}}

{{{Lx-Hx=TP-HP}}}

{{{(L-H)x=P(T-H)}}}

{{{x=P((T-H)/(L-H))}}}
and you know that in this form, numerator and denominator of the fraction are both negative, so simply
{{{x=P((H-T)/(H-L))}}}



The question asked for essentially  {{{highlight((H-T)/(H-L))}}}.


Substitute your given values.