Question

How much orange pekoe tea costing $6.00 per pound should be mixed with green tea costing $5.00 per pound to get a mixture of 30 pounds costing $5.25 per pound?

Answer 1

7.5 pounds

Explanation:

How much orange pekoe tea costing $6.00 per pound should be mixed with green tea costing $5.00 per pound to get a mixture of 30 pounds costing $5.25 per pound?

We have two systems of equations

Let the number of pounds of pekoe tea be represented by p

The number of pounds of green tea be represented by g

Hence:

p + g = 30 ...... Equation 1

p = 30 - g

$6 × p + $5 × g = 30 × $5.25

6p + 5g = 157.5.........Equation 2

We substitute 30 - g for p in Equation 2

6(30 - g) + 5g = 157.5

180 - 6g + 5g = 157.5

-6g + 5g = 157.5 - 180

-g = -22.5

g = 22.5 pounds

Solving for p

p = 30 - g

p = 30 - 22.5

p = 7.5 pounds

Hence, the number of pounds of pekoe tea = 7.5 pounds