A tea manufacturer wants to make 10,000 pounds of a signature tea blend out of t

Question

A tea manufacturer wants to make 10,000 pounds of a signature tea blend out of three types of tea leaves. The three component leaves are Earl Grey, English Breakfast and Jasmine, which cost $2.40, $2.60, and $2 per pounds respectively. The manufacturer wants to spend $21,000 on purchasing enough leaves to make 10,000 pounds of this signature blend. The only other requirement is that an equal number of Earl Grey and English Breakfast leaves must be used in the blend. Find a system of linear equations that describes these constraints. Determine whether there is a combination of the three types of tea leaves that will satisfy all criteria.

Explanation / Answer

Let X represent the number of pounds of Earl Grey

Let Y represent the number of pounds of English Breakfast

Let Z represent the number of pounds of Jasmine.

X=Y

X+Y+Z = 10,000

2.4X + 2.6Y + 2.0Z =21,000

Substituting X for Y in equations 2 and 3 we get:

X+X+Z = 10,000-------------------> 2X + Z = 10,000---------->4X + 2Z = 20,000

2.4X+2.6X+2.0Z = 21,000------>5X + 2Z = 21,000--------->5X + 2Z = 21,000

X = 1,000

Y = 1,000

Z = 8,000

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.