The manager of a store selling tea plans to mix a more expensive tea that costs $5 per pound with a less expensive tea that costs $2 per pound to create a 140-pound blend that will sell for $3.80 per pound. How many pounds of each type of tea are required?
5 x + 2(140 - x) = 3.8 * 140
To solve this problem, we can set up a system of equations based on the given information.
Let x represent the number of pounds of the more expensive tea that will be used.
Let y represent the number of pounds of the less expensive tea that will be used.
We are given the following information:
1. The more expensive tea costs $5 per pound.
2. The less expensive tea costs $2 per pound.
3. The total weight of the blend is 140 pounds.
4. The average price of the blend is $3.80 per pound.
Based on this information, we can write the following equations:
Equation 1: x + y = 140 (since the total weight of the blend is 140 pounds)
Equation 2: (5x + 2y) / 140 = 3.80 (since the average price of the blend is $3.80 per pound)
To solve this system of equations, we can use substitution or elimination method.
Let's solve using the substitution method:
Rearrange Equation 1 to solve for x: x = 140 - y
Replace x in Equation 2 with the value from the rearranged Equation 1: (5(140 - y) + 2y) / 140 = 3.80
Simplify the equation: (700 - 5y + 2y) / 140 = 3.80
Simplify further: (700 - 3y) / 140 = 3.80
Multiply both sides of the equation by 140 to eliminate the fraction: 700 - 3y = 140 * 3.80
Simplify: 700 - 3y = 532
Subtract 700 from both sides: -3y = -168
Divide by -3: y = 56
Now, substitute y = 56 into the rearranged Equation 1: x = 140 - 56
Simplify: x = 84
Therefore, in order to create a 140-pound blend that sells for $3.80 per pound, the manager needs 84 pounds of the more expensive tea and 56 pounds of the less expensive tea.