How many pounds of the Earl Grey tea and Orange Pekoe tea are​ required?

Question

The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $5 per pound with some Orange Pekoe tea that sells for $3 per pound to get 400 pounds of the new blend. The selling price of the new blend is to be $4.50 per​ pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are​ required?

Answer 1

The money from the new blend will be 400 times $4.50. The total pounds of the new tea is 400. Let e be the pounds of Earl Grey tea and P be the pounds of Orange Pekoe tea. Two equations are made: one for money and one for pounds of tea. The money equation is 5E + 3 P = 400 * 4.50 ; the money from the new tea sales equals the money from the new. The pound equation is E + P = 400; 400 pounds to be made.

Subtracting P from each side and solving for E in the pound equation E = 400- P.

Substitute in the money equation: 5 ( 400-P) + 3 P =400 * 4.50.

Multiply through the ( ): 2000 - 5P + 3 P = 1800

Subtract 2000 from each side and combine terms: - 2 P = -200

Divide by -2: P = 100; Orange Pekoe Tea 100 pounds

Substitute in to the E + P = 400 equation and find: E = 300; Earl Grey Tea 300 pounds

Answer 2

Given 400 lb of tea mix at $4.50 / lb. Earl grey alone is $5 / lb and Orange Pekoe alone is $3 / lb.

Total revenue will be 400 x $4.50 = $1800.

The same revenue is expected if each tea is sold alone.

$1800 for Earl Grey alone requires 1800/5 = 360 lb of that tea

$1800 for Orange Pekoe alone rquires 1800/3 = 600 lb of that tea.

To find the amounts of Earl Grey (G) and Orange Pekoe (P) teas required to make the blend, note that the the value of 400 lb of blend can be determined as $5 x lb of Earl Grey + $3*(400-G), where 400 lb of blend - lb or Earl Grey = lb of Orange Pekoe.

$1800 = $5G + $3*(400 - P) ==> $5G + $1200 - $3G ==> $1800 = $2G + $1200

Subtract $1200 from both sides

$600 = $2G

Divide by $2 to get G = 300lb of Earl Grey. @ $5/lb the value ie $1500

P = 400lb - 300lb = 100lb of Orange Pekoe. @ $3/lb the value is $300.

Total value of the blend is $1500 + $300 = $1800.

Answer 3

The last sentence in the problem is confusing since we have no information about how much is sold at each price!

Let E=# of Earl Grey and P=# of Orange Pekoe

E+P=400

5E+3P=4.5*400=1800

Multiply first equation by 3 and subtract it from the 2nd equation: :2E=600

E=300

P=100

Use these answers to check that they satisfy the requirements of the problem.